Concentrating particles in a microfluidic device

ABSTRACT

A microfluidic device includes: a first microfluidic channel; a second microfluidic channel extending along the first microfluidic channel; and a first array of islands separating the first microfluidic channel from the second microfluidic channel, in which each island is separated from an adjacent island in the array by an opening that fluidly couples the first microfluidic channel to the second microfluidic channel, in which the first microfluidic channel, the second microfluidic channel, and the islands are arranged so that a fluidic resistance of the first microfluidic channel increases relative to a fluidic resistance of the second microfluidic channel along a longitudinal direction of the first microfluidic channel such that, during use of the microfluidic device, a portion of a fluid sample flowing through the first microfluidic channel passes through one or more of the openings between adjacent islands into the second microfluidic channel.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application is a continuation of U.S. application Ser. No.16/211,362, filed on Dec. 6, 2018, which is a continuation of U.S.application Ser. No. 14/931,421, filed on Nov. 3, 2015, which claims thebenefit of U.S. Provisional Application No. 62/074,213, filed Nov. 3,2014, and U.S. Provisional Application No. 62/074,315, filed Nov. 3,2014, each of which is incorporated herein by reference in its entirety.

TECHNICAL FIELD

The present disclosure relates to concentrating particles in amicrofluidic device.

BACKGROUND

Particle separation and filtration have been used in numerousapplications across industries and fields. Examples of such applicationsinclude chemical process and fermentation filtration, waterpurification/wastewater treatment, sorting and filtering components ofblood, concentrating colloid solutions, and purifying and concentratingenvironmental samples. Various macro-scale techniques have beendeveloped for use in these applications including methods such ascentrifugation and filter-based techniques. Typically, such techniquesrequire systems that are large, bulky, and expensive and have complexmoving components.

In certain cases, micro-scale techniques offer advantages overmacro-scale techniques, in that scaling down allows the use of uniquehydrodynamic effects for particle sorting and filtration, and thuseliminates the need for large systems with complex moving components.Moreover, micro-scale techniques offer the possibility of portabledevices capable of performing sorting and filtration at much lower costthan larger macro-scale systems. However, typical micro-scale sortingand filtration devices may be limited in the amount of fluid they canhandle over a specified period of time (i.e., low throughput),potentially placing such devices at a disadvantage to their macro-scalecounterparts.

SUMMARY

The present disclosure is based, at least in part, on the discovery thatif one carefully controls the geometries and dimensions of microfluidicdevices one can manipulate not only the position of particles suspendedwithin a fluid sample, but also portions of the fluid itself to enablesubstantial increases in particle concentration for large quantities ofthe fluid sample or to filter fluid samples of undesired particles. Forexample, careful control of the geometries and dimensions of amicrofluidic device can, in certain implementations, be used to alterthe concentration of particles within a fluid sample through shiftingthe particles across fluid streamlines.

In particular, through a combination of fluid extraction and inertiallift forces, it is possible to manipulate both particles and the fluidthat carries them to alter the concentration of one or more types ofparticles within the fluid. For instance, a fluid containing particlesmay be introduced into a microfluidic channel having an array of rigidisland structures separating the channel from an adjacent microfluidicchannel. As fluid is extracted from the first microfluidic channel intothe second microfluidic channel through gaps between the islandstructures, the particles are drawn nearer to the island structures. Asthe particles reach nearer to the island structures, the particlesexperience an inertial lift force away from the direction of fluidextraction such that the particles cross fluid streamlines and remain inthe first microfluidic channel while the amount of fluid in the firstmicrofluidic channel decreases (i.e., leading to an increase in particleconcentration).

The combination of fluid extraction and inertial lift force enables anumber of ways to manipulate fluids and particles. For example,particles may be shifted from one fluid to another. In another example,the combined fluid extraction and inertial lift forces may be used tofocus particles to desired positions within a microfluidic channel.These and other applications may be scaled over large numbers ofmicrofluidic channels to achieve high throughput increases in particleconcentration with low device fabrication costs.

In general, in one aspect, the subject matter of the present disclosurecan be embodied in microfluidic devices that have a first microfluidicchannel, a second microfluidic channel extending along the firstmicrofluidic channel, and a first array of islands separating the firstmicrofluidic channel from the second microfluidic channel, in which eachisland is separated from an adjacent island in the array by an openingthat fluidly couples the first microfluidic channel to the secondmicrofluidic channel, in which the first microfluidic channel, thesecond microfluidic channel, and the islands are arranged so that afluidic resistance of the first microfluidic channel changes relative tothe fluidic resistance of the second microfluidic channel along alongitudinal section of the first microfluidic channel or the secondmicrofluidic channel such that, during use of the microfluidic device, aportion of a fluid sample flowing in the first microfluidic channel orthe second microfluidic channel is siphoned through one or more of theopenings between adjacent islands.

In general, in another aspect, the subject matter of the presentdisclosure can be embodied in microfluidic devices including: a firstmicrofluidic channel; a second microfluidic channel extending along thefirst microfluidic channel; and a first array of islands separating thefirst microfluidic channel from the second microfluidic channel, inwhich each island is separated from an adjacent island in the array byan opening that fluidly couples the first microfluidic channel to thesecond microfluidic channel, in which the first microfluidic channel,the second microfluidic channel, and the islands are arranged so that afluidic resistance of the first microfluidic channel increases relativeto a fluidic resistance of the second microfluidic channel along alongitudinal direction of the first microfluidic channel such that,during use of the microfluidic device, a portion of a fluid sampleflowing through the first microfluidic channel passes through one ormore of the openings between adjacent islands into the secondmicrofluidic channel, and in which a width of the first microfluidicchannel repeatedly alternates between a narrow region and an enlargedregion along the longitudinal direction of the first microfluidicchannel.

Implementations of the devices may have one or more of the followingfeatures. For example, in some implementations, the first microfluidicchannel, the second microfluidic channel and the first array of islandsare further arranged to, during use of the microfluidic device,substantially prevent multiple first types of particles in the fluidsample from propagating with the fluid through one or more of theopenings between adjacent islands into the second microfluidic channel.The first microfluidic channel, the second microfluidic channel and thefirst array of islands can be arranged to, during use of themicrofluidic device, impart an inertial lift force on the plurality ofthe first type of particle to prevent the multiple first types ofparticle from propagating with the fluid through one or more of theopenings between adjacent islands into the second microfluidic channel.The first microfluidic channel, the second microfluidic channel and thefirst array of islands can be arranged to, during use of themicrofluidic device, impart a bumping force on the plurality of thefirst type of particle to prevent the multiple first types of particlefrom propagating with the fluid through one or more of the openingsbetween adjacent islands into the second microfluidic channel. Across-sectional area of each opening through which the fluid passes fromthe first microfluidic channel into the second microfluidic channel canbe larger than the first type of particle.

In some implementations, the increase in fluidic resistance of the firstchannel relative to the fluidic resistance of the second channelincludes a change in a cross-sectional area of the first microfluidicchannel or the second microfluidic channel along the longitudinaldirection of the first microfluidic channel. The change incross-sectional area of the second microfluidic channel can include anincrease in the cross-sectional area of the second microfluidic channelrelative to the cross-sectional area of the first microfluidic channelalong the longitudinal direction. The change in cross-sectional area ofthe first microfluidic channel can include a decrease in thecross-sectional area of the first microfluidic channel relative to thecross-sectional area of the second microfluidic channel along thelongitudinal direction.

In some implementations, the array of islands includes multiple openingsand a size of the openings increases along the longitudinal direction ofthe first microfluidic channel. A size of each opening in the array canbe greater than a size of a previous opening in the array.

In some implementations, at least one of the enlarged regions is alignedwith a corresponding opening between the islands. The first microfluidicchannel can have an approximately sinusoidal shape.

In some implementations, for each island, a contour of a first side ofthe island substantially matches a contour of a wall of the firstchannel facing the first side of the island.

In some implementations, the microfluidic devices further includes: athird microfluidic channel extending along the first microfluidicchannel; and a second array of islands separating the first microfluidicchannel and the third microfluidic channel such that the firstmicrofluidic channel is between the second and third microfluidicchannels, in which each island in the second array is separated from anadjacent island in the second array by an opening that fluidly couplesthe first microfluidic channel to the third microfluidic channel, and inwhich the third microfluidic channel, the first microfluidic channel,and the second array of islands are arranged so that the fluidicresistance of the first microfluidic channel increases relative to afluidic resistance of the third microfluidic channel along thelongitudinal direction of the first microfluidic channel such that,during use of the microfluidic device, a portion of a fluid sampleflowing through the first microfluidic channel passes through one ormore of the openings between adjacent islands of the second array ofislands into the third microfluidic channel. The increase in fluidicresistance of the first channel relative to the fluidic resistance ofthe third channel can include a change in a cross-sectional area of thefirst microfluidic channel or the third microfluidic channel along thelongitudinal direction of the first microfluidic channel.

In some implementations, the microfluidic devices further include: athird microfluidic channel extending along the second microfluidicchannel; and a second array of islands separating the secondmicrofluidic channel and the third microfluidic channel such that thesecond microfluidic channel is between the first and third microfluidicchannels, in which each island in the second array is separated from anadjacent island in the second array by an opening that fluidly couplesthe second microfluidic channel to the third microfluidic channel, andin which the third microfluidic channel, the second microfluidicchannel, and the second array of islands are arranged so that a fluidicresistance of the third microfluidic channel increases relative to thefluidic resistance of the second microfluidic channel along alongitudinal direction of the third microfluidic channel such that,during use of the microfluidic device, a portion of a fluid sampleflowing through the third microfluidic channel passes through one ormore of the openings between adjacent islands of the second array ofislands into the second microfluidic channel.

In some implementations, the microfluidic devices further include: afirst inlet channel; and a second inlet channel, in which each of thefirst inlet channel and the second inlet channel is fluidly coupled tothe first microfluidic channel and the second microfluidic channel. Insome implementations, the microfluidic devices further include: a firstinlet channel; and a second inlet channel, in which each of the firstinlet channel and the second inlet channel is fluidly coupled to thefirst microfluidic channel, the second microfluidic channel and thethird microfluidic channel.

In some implementations, the first microfluidic channel, the secondmicrofluidic channel, and the first array of islands correspond to acombined inertial focusing and fluid siphoning region, in which themicrofluidic device includes multiple combined inertial focusing andfluid siphoning regions arranged in parallel.

In some implementations, the microfluidic devices further include one ormore magnets establishing a magnetic field gradient across the firstand/or second microfluidic channel.

In some implementations, the first microfluidic channel and the secondmicrofluidic channel are arranged in a spiral configuration.

In some implementations, the first array comprises at least threeislands.

In general, in another aspect, the subject matter of the presentdisclosure can be embodied in microfluidic devices including: a firstmicrofluidic channel; a second microfluidic channel extending along thefirst microfluidic channel; and a first array of islands separating thefirst microfluidic channel from the second microfluidic channel, inwhich each island is separated from an adjacent island in the array byan opening that fluidly couples the first microfluidic channel to thesecond microfluidic channel, in which the first microfluidic channel,the second microfluidic channel, and the islands are arranged so that afluidic resistance of the first microfluidic channel increases relativeto a fluidic resistance of the second microfluidic channel along alongitudinal direction of the first microfluidic channel such that,during use of the microfluidic device, a portion of a fluid sampleflowing through the first microfluidic channel passes through one ormore of the openings between adjacent islands into the secondmicrofluidic channel.

In general, in another aspect, the subject matter of the presentdisclosure can be embodied in methods of changing a concentration ofparticles within a fluid sample, the methods including: flowing a fluidsample containing multiple first types of particle into a microfluidicdevice, in which the microfluidic device includes a first microfluidicchannel, a second microfluidic channel extending along the firstmicrofluidic channel, and a first array of islands separating the firstmicrofluidic channel from the second microfluidic channel, in which thefirst microfluidic channel, the second microfluidic channel, and theislands are arranged so that a fluidic resistance of the firstmicrofluidic channel increases relative to a fluidic resistance of thesecond microfluidic channel along a longitudinal direction of the firstmicrofluidic channel such that a portion of the fluid sample flowingthrough the first microfluidic channel passes through one or more of theopenings between adjacent islands into the second microfluidic channelwithout the first type of particle, and in which a width of the firstmicrofluidic channel repeatedly alternates between a narrow region andan enlarged region along the longitudinal direction of the firstmicrofluidic channel such that inertial focusing causes the multiplefirst types of particle to be focused to one or more streamlines of thefluid sample within the first channel.

Implementations of the methods may have one or more of the followingfeatures. For example, in some implementations, a concentration of thefirst type of particle increases within the fluid sample remaining inthe first microfluidic channel.

In some implementations, the microfluidic device includes a thirdmicrofluidic channel extending along the second microfluidic channel anda second array of islands that separates the second microfluidic channelfrom the third microfluidic channel, in which a fluidic resistance ofthe third microfluidic channel increases relative to the fluidicresistance of the second microfluidic channel along a longitudinaldirection of the third microfluidic channel such that a portion of thefluid sample flowing through the third microfluidic channel passesthrough openings between islands in the second array into the secondmicrofluidic channel without the first type of particle, and in which awidth of the third microfluidic channel repeatedly alternatives betweena narrow region and an enlarged region along the longitudinal directionof the third microfluidic channel such that inertial focusing causes theplurality of the first type of particle to be focused to one or morestreamlines of the fluid sample within the third channel. Aconcentration of the first type of particle can increase within thefluid sample remaining in the third microfluidic channel.

In some implementations, the microfluidic device includes a thirdmicrofluidic channel extending along the first microfluidic channel anda second array of islands that separates the first microfluidic channelfrom the third microfluidic channel, in which the fluidic resistance ofthe first microfluidic channel increases relative to the fluidicresistance of the third microfluidic channel along the longitudinaldirection of the third microfluidic channel such that a portion of thefluid sample flowing through the first microfluidic channel passesthrough the openings between islands in the second array into the thirdmicrofluidic channel without the first type of particle.

In some implementations, at least one of the first type of particles isbound to a magnetic bead, and the methods further include exposing thefluid sample to a magnetic field gradient, in which the magnetic fieldgradient guides the at least one particle bound to a magnetic bead awayfrom one or more of the openings between adjacent islands in the firstarray.

In some implementations, the fluid sample contains multiple second typesof particle, in which the second types of particles are bound tomagnetic beads, and the methods further include exposing the fluidsample to a gradient in a magnetic field, in which the gradient in themagnetic field deflects the second type of particles that are bound tomagnetic beads away from the first type of particle such that the secondtype of particle propagates with the fluid portion through one or moreof the openings of the first array.

In some implementations, the fluid sample has a dynamic viscosity thatvaries with shear rate, and the method further includes driving thefluid sample through the first microfluidic channel at a volumetric flowrate that results in the formation of a localized streamline at or neara center of the first microfluidic channel, in which the multiple firsttypes of particles are focused into the localized streamline. The fluidsample can include a drag-reducing polymer added to a Newtonian fluid.The drag-reducing polymer can include hyaluronic acid (HA).

In some implementations, the particle to fluid concentration at anoutput of the first microfluidic channel is greater than 10 times andless than 5000 times the particle to fluid concentration prior toentering the first microfluidic channel.

In some implementations, the methods further include collecting themultiple first types of particle at an output of the first microfluidicchannel.

In some implementations, the first type of particle has an averagediameter between about 1 μm and about 100 μm.

In some implementations, a size of each opening between the islands isgreater than the average diameter of the first type of particle.

Implementations of the subject matter described herein provide severaladvantages. For example, in some implementations, the subject matterdescribed herein can be used to isolate particles within a continuouslyflowing fluid, focus particles within a continuously flowing fluid,increase the concentration of particles within a continuously flowingfluid without the need for centrifugation, and/or obtain purified fluidsamples with low particle concentration. In some implementations, thesubject matter described herein can be used to shift particles from onefluid to another fluid. The continuous flow microfluidic techniquesdescribed herein may offer high volumetric capacity and throughput,substantial and tunable fluid volume reduction, and high particle yieldswith inexpensive and simple instruments that can be implemented intovarious point-of-care devices. In particular, the presently describedtechniques may offer significant advantages over existing centrifugationtechniques, especially in applications where the size and expense ofcentrifugation is prohibitive. In some implementations, the presentlydescribed techniques also may provide streamlined processing and simpleintegration with other microfluidic modules. For clinical applications,the systems described herein may be configured as both self-containedand disposable. In contrast, for bioprocessing/industrial applications,the devices may be configured for continuous flow/processing.

For the purposes of this disclosure, channel refers to a structure inwhich a fluid may flow.

For the purposes of this disclosure, microfluidic refers to a fluidicsystem, device, channel, or chamber that generally have at least onecross-sectional dimension in the range of about 10 nm to about 10 mm.

For the purposes of this disclosure, the terms gap or opening refer toan area in which fluids or particles may flow. For example, a gap oropening may be a space between two obstacles in which fluids flow.

For the purposes of this disclosure, rigid island structure refers to aphysical structure through which a particle generally cannot penetrate.

For the purposes of this disclosure, volume reduction means processing asuspension of cells/particles such that the product of the process has ahigher concentration (and therefore smaller volume) of thecells/particles than the input.

For the purposes of this disclosure, a particle-free layer is understoodto be an elongated region of a continuously flowing fluid sample withina microfluidic device that is substantially free of one or moredifferent types of particles.

For the purposes of this disclosure, absolute particle yield isunderstood to mean the total number of particles in the product dividedby the total number particles in the input.

For the purposes of this disclosure, relative yield is understood tomean the total number of particles in the product divided by the totalnumber of particles in the output (i.e., product plus waste).

For the purposes of this disclosure, length fraction is understood tomean the fraction of that stream occupied by particles (as opposed tospace between particles).

For the purposes of this disclosure, fluidic resistance refers to theratio of pressure drop across a channel (e.g., a microfluidic channel)to the flow rate of fluid through the channel.

Particles within a sample can have any size which allows them totransported within the microfluidic channel. For example, particles canhave an average hydrodynamic size that is between 1 μm and 100 μm. Theparticle size is limited only by channel geometry; accordingly,particles that are larger and smaller than the above-described particlescan be used. The size of particles (e.g., cells, eggs, bacteria, fungi,virus, algae, any prokaryotic or eukaryotic cells, organelles, exosomes,droplets, bubbles, pollutants, precipitates, organic and inorganicparticles, magnetic beads, and/or magnetically labeled analytes), suchas the average hydrodynamic particle size or average diameter, can bedetermined using standard techniques well known in the field.

Unless otherwise defined, all technical and scientific terms used hereinhave the same meaning as commonly understood by one of ordinary skill inthe art to which this invention belongs. Although methods, materials,and devices similar or equivalent to those described herein can be usedin the practice or testing of the present invention, suitable methods,materials and devices are described below. All publications, patentapplications, patents, and other references mentioned herein areincorporated by reference in their entirety. In case of conflict, thepresent specification, including definitions, will control. In addition,the materials, methods, and examples are illustrative only and notintended to be limiting.

The details of one or more embodiments are set forth in the accompanyingdrawings and the description below. Other features, objects, and will beapparent from the description, drawings, and claims.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a schematic illustrating a top view of an example of amicrofluidic device capable of shifting the position of particles withinand across fluid streamlines.

FIG. 2 is a schematic illustrating a top view of an example of a devicefor particle and fluid shifting, in which a particle shifting areaincludes two different microfluidic channels for extracting fluid.

FIG. 3 is a schematic illustrating a top view of an example of a devicein which particle shifting concentrates particles from one stream alongtwo different microfluidic channels.

FIG. 4 is a schematic illustrating a top view of an example of a devicecapable of shifting particles from one carrier fluid to another carrierfluid.

FIG. 5 is a schematic illustrating a top view of an example of aparticle shifting area of a microfluidic device that relies on inertialfocusing and fluid extraction

FIG. 6A is a schematic depicting how fluid streamlines may behave withina microfluidic device that combines inertial focusing with repeatedfluid extraction.

FIG. 6B includes plots of simulated fluid flow for differentcross-sections of the device shown in FIG. 6A.

FIG. 7 is a plot that depicts the cell free flow fraction as function ofthe number of siphon-focusing unit pairs for the device structure shownin FIG. 6B

FIG. 8 is a schematic that illustrates an example of a microfluidicsystem that includes a particle shifting area.

FIGS. 9A-9C are schematics illustrating examples of microfluidic systemsin which a particle shifting area is fluidly coupled to amagnetophoresis area.

FIGS. 9D-9F are schematics illustrating examples of microfluidic systemsin which a particle shifting area and a magnetophoresis area arecombined.

FIG. 10 is a plot of cell-free fraction versus sample flow rate througha microfluidic device.

FIGS. 11A-11D are photographs of fluorescently tagged particles flowingthrough focusing-siphoning units of a microfluidic device for differentsiphon percentages.

FIG. 12 is a plot of relative white blood cell yield versus flow rate.

FIG. 13 is a plot of relative particle yield in a microfluidic deviceversus flow-rate.

FIG. 14 is a plot illustrating the relative yield of white blood cellswithin a microfluidic device for different input concentrations.

FIG. 15 is a schematic that illustrates a top view of a design of amicrofluidic system.

FIG. 16 is a schematic illustrating a top view of an example particleand fluid shifting area of a microfluidic device.

DETAILED DESCRIPTION

Interactions among particles within a fluid (e.g., cells, e.g., bloodcells in general as well as fetal blood cells in maternal blood, bonemarrow cells, and circulating tumor cells (CTCs), sperm, eggs, bacteria,fungi, virus, algae, any prokaryotic or eukaryotic cells, cell clusters,organelles, exosomes, droplets, bubbles, pollutants, precipitates,organic and inorganic particles, beads, bead labeled analytes, magneticbeads, and/or magnetically labeled analytes), the fluids in which theparticles travel (e.g., blood, aqueous solutions, oils, or gases), andrigid structures can be controlled to perform various microfluidicoperations on both the particles and fluid. In particular, suchinteractions may entail shifting the particles across fluid streamlines,through either the displacement of the fluid or the particlesthemselves. Examples of microfluidic operations that can be performed bycontrolling these interactions include, but are not limited to,increasing the concentration of particles in a carrier fluid, reducingthe volume of a fluid sample, reducing the concentration of particleswithin a fluid, shifting particles from one carrier fluid to anotherfluid, separating particles within a fluid based on particle size (e.g.,average diameter), focusing particles within a carrier fluid to asingle-streamline (or to multiple different streamlines), precisepositioning of particles at any position within a micro-channel, andmixing (defocusing) particles. Moreover, any of the above operations canbe executed simultaneously with other techniques (e.g., magneticsorting) to enhance the operation's effectiveness.

Several different mechanisms can be employed to create the forcescapable of shifting particles across fluid streamlines. Any of thefollowing techniques may be used individually or in combination toinduce particle shifting within a fluid. A first type of force isreferred to as “bumping” (also called deterministic lateral displacement(DLD)). Bumping is direct interaction between a rigid wall of astructure and a particle that arises due to the size of the particlerelative to the wall. Since the center of a particle having radius r_(p)cannot pass closer to an adjacent structure than r_(p), if the particlecenter lies on a streamline that is less than r_(p) from the structure,the particle will be bumped out by the structure to a distance that isat least r_(p) away. This bumping may move the particle across fluidstreamlines.

Another type of force is called inertial lift force (also known as wallforce or wall induced inertia). The inertial lift force is a fluidicforce on a particle that arise when then the particle and fluid flownear a wall. Though not well understood, the inertial lift force is arepulsive force arising due to a flow disturbance generated by theparticle when the particle nears the wall. In contrast to bumping, theinertial lift force is a fluidic force on a particle, not a force due tocontact with a rigid structure. A particle flowing near a micro-channelwall experiences an inertial lift force normal to the wall. At high flowrates, the inertial lift force is very strong and can shift the particleacross streamlines.

Another type of force is a result of pressure drag from Dean flow.Microfluidic channels having curvature can create additional drag forceson particles. When introducing the curvature into rectangular channels,secondary flows (i.e., Dean flow) may develop perpendicular to thedirection of a flowing stream due to the non-uniform inertia of thefluid. As a result, faster moving fluid elements within the center of acurving channel can develop a larger inertia than elements near thechannel edges. With high Dean flow, drag on suspended particles withinthe fluid can become significant.

Another type of particle shifting occurs with high Stokes number flow.The Stokes number (Stk) describes how quickly a particle trajectorychanges in response to a change in fluid trajectory. For Stk greaterthan 1, a lag exists between the change in fluid trajectory and thechange in particle trajectory. Under high Stokes flow conditions (e.g.,a Stokes number greater than about 0.01), changing the fluid flowdirection can be used to force particles across streamlines. Furtherdetails on Dean flow and high Stokes number can be found, for example,in U.S. Pat. No. 8,186,913, which is incorporated herein by reference inits entirety. In both high Stokes flow applications and Dean flowapplications, the fluid displacement causes the particles to cross fluidstreamlines.

Other techniques for shifting particles include viscoelastic andinertio-elastic focusing. Details on those methods can be found in“Sheathless elasto-inertial particle focusing and continuous separationin a straight rectangular microchannel,” Yang et al., Lab Chip (11),266-273, 2011, “Single line particle focusing induced by viscoelasticityof the suspending liquid: theory, experiments and simulations to designa micropipe flow-focuser,” D'Avino et al., Lab Chip (12), 1638-1645,2012, and “Inertio-elastic focusing of bioparticles in microchannels athigh throughput,” Lim et al., Nature Communications, 5 (5120), 1-9,2014, each of which is incorporated herein by reference in its entirety.

The foregoing techniques for shifting particles are “internal,” in thatthey use fluid flow and/or structures of the microfluidic channel itselfto generate the forces necessary to shift particles across streamlines.In some cases, other external mechanisms can also be used in conjunctionwith one or more of the internal forces to alter the course of particlestraveling within a fluid. For example, in some cases, externally appliedmagnetic forces, gravitational/centrifugal forces, electric forces, oracoustic forces may be used to cause a shift in particle position acrossfluid streamlines. Further information on how to apply such forces canbe found, e.g., in WO 2014/004577 titled “Sorting particles using highgradient magnetic fields,”, U.S. Pat. No. 7,837,040 titled “Acousticfocusing,” WO 2004/074814 titled “Dielectrophoretic focusing,” and“Microfluidic, Label-Free Enrichment of Prostate Cancer Cells in BloodBased on Acoustophoresis,” Augustsson et al., Anal. Chem. 84(18), Sep.18, 2012,

The present disclosure focuses primarily on combining inertial liftforces with periodic fluid extraction to shift particles across fluidstreamlines to modify the concentration of and/or to filter particles ina fluid, though it should be understood that inertial lift forces may bereplaced with or used in addition to other forces, such as thosedescribed above. As an example of combined inertial, particle containingfluids may be introduced into a microfluidic channel having an array ofrigid island structures separating the channel from an adjacentmicrofluidic channel. As fluid is extracted from the first microfluidicchannel into the second microfluidic channel through gaps between theisland structures, the particles are drawn nearer to the islandstructures. As the particles reach nearer to the island structures, theparticles experience a repulsive force (e.g., an inertial lift force)away from the direction of fluid extraction such that the particlescross fluid streamlines. The combination of fluid extraction and therepulsive forces may be used to perform positioning of particles,increasing the concentration of particles within a fluid, decreasing theconcentration of particles within a fluid, particle mixing, fluidmixing, and/or shifting of fluids across particle streams, among otheroperations.

The mechanisms for shifting particles may be size-based and thereforecan be used to perform size-based manipulation of particles (e.g., basedon the average diameter of the particles). Through the repeated shiftingof particles and/or displacement of fluid using any of theabove-mentioned techniques, various different microfluidic operationsmay be performed, such as focusing particles to one or more fluidstreamlines, increasing the concentration of particles within a fluid,performing volume reduction of a fluid, filtering particles from afluid, and/or mixing different particles from different fluid streams.In general, “focusing” particles refers to re-positioning the particlesacross a lateral extent of the channel and within a width that is lessthan the channel width. For example, the techniques disclosed herein canlocalize particles suspended in a fluid within a length of the channelhaving a width of 1.05, 2, 4, 6, 8, 10, 20, 30, 40, 50, 60, 70, 80, 90,or 100 times the average diameter of the particles. In someimplementations, the particles are focused to a streamline of a fluid.In some implementations, a streamline defines a width that issubstantially equal to or slightly greater than a hydraulic diameter ofthe particle. Particles may have various sizes including, but notlimited to, between about 1 μm and about 100 μm in average diameter.

Altering Particle Concentration Using Inertial Lift Forces

FIG. 1 is a schematic that illustrates a top view of an example of amicrofluidic device 100 capable of shifting the position of particles102 across fluid streamlines while the fluid propagates through themicrofluidic device 100. As will be explained, the particle shiftingacross fluid streamlines relies on the inertial lift forces experiencedby particles as fluid is periodically extracted from a microfluidicchannel, though other repulsive forces may be used in place of or inaddition to inertial lift forces. For reference, a Cartesian coordinatesystem is shown, in which the x-direction extends into and out of thepage.

During operation of the device 100, a fluid carrying the particles 102is introduced through an inlet microfluidic channel 104. In this andother implementations of the particle shifting devices, the fluid can beintroduced through the use of a pump or other fluid actuation mechanism.The inlet channel 104 splits into two different fluid flow channels(second microfluidic channel 106 and first microfluidic channel 108substantially parallel to the second microfluidic channel 106) that areseparated by a 1-dimensional array of rigid island structures 110. The1-dimensional array of island structures 110 extends substantially inthe same direction as the flow of the fluid through the second and firstmicrofluidic channels. Each island structure 110 in the array isseparated from an adjacent island 110 by an opening or gap 114 throughwhich fluid can flow. Each gap 114 in the example of FIG. 1 has the samedistance between adjacent islands 110. In other implementations,different gaps can have different distances between adjacent islands110. For example, in some implementations, a length of each subsequentopening (e.g., as measured along the fluid propagation direction—thez-direction in FIG. 1) in the first array is greater than a size of aprevious opening in the array. Furthermore, although a 1-dimensionalarray is shown in FIG. 1, the islands 110 may be arranged in differentconfigurations including, for example, a two-dimensional array ofislands. The boundaries of the fluid flow regions within themicrofluidic channels are defined by the device walls 112 and the wallsof the islands 110.

As the fluid propagates substantially along the z-direction (i.e., thelongitudinal direction) from the inlet channel 104 to the channels (106,108), particles 102 experience a force (in this example, an inertiallift force) that causes the particles 102 to shift across fluidstreamlines and travel along the first microfluidic channel 108. Theseinertial lift forces are in the negative y-direction (see short arrowsadjacent to each particle 102 in FIG. 1).

For instance, when a particle 102 is located in the inlet channel 104and approaches the top wall 112, the particle experiences an inertiallift force that pushes the particle down toward the first microfluidicchannel 108. Once in the first microfluidic channel 108, the particle102 may approach a wall of the first island 110, such that it againexperiences an inertial lift force pushing the particle 102 down,maintaining the particle within the first microfluidic channel 108. Therepeated application of the inertial lift force to the particle 102 ineach of the “particle shift” regions shown in FIG. 1 thus serves toseparate/filter the particle from the fluid propagating through thesecond microfluidic channel 106.

At the same time, portions of the fluid traveling in the firstmicrofluidic channel 108 are extracted (e.g., siphoned)/pass into thesecond microfluidic channel at one or more “fluid shift” regions (seeFIG. 1) in the device 100. In the example of FIG. 1, each fluid shiftregion corresponds to an opening or gap that extends between the firstmicrofluidic channel 108 and the second microfluidic channel 106. Each“fluid shift” region primarily allows fluid to be extracted from thefirst microfluidic channel 108 into the second microfluidic channel 106.The movement of fluid into the gaps tends to pull the particles 102toward the gaps as well, since the particles follow the fluidstreamlines. However, as the particles move closer to the gaps 114, theyapproach the island structures 112, which impart an inertial lift forcecausing the incident particles to cross fluid streamlines in a directionaway from the gaps 114. That is, the particles 102 shift from a fluidstreamline passing into the second microfluidic channel 106 to a fluidstreamline that continues to flow in the first microfluidic channel 108.As a result, the particles 102 continue to propagate in the firstmicrofluidic channel 108 and are not shifted into the secondmicrofluidic channel 106 with the fluid. If there were no fluid shiftingfrom the first microfluidic channel 108 to the second microfluidicchannel 106, the particles would migrate as a result of inertialfocusing toward equilibrium focusing positions where the inertial liftforce and shear gradient force are balanced. However, by shifting thefluid across the channels, the particles 102 tend to follow the fluidtoward areas where the inertial lift force is much stronger than theshear gradient force, thus causing the particles to shift acrossstreamlines in a very efficient and controlled manner.

In the present example, the fluid is extracted through the fluid shiftregions as a result of decrease in fluidic resistance along alongitudinal section of the fluid shift region. That is, for a fluid ofconstant viscosity, the gaps 114 between adjacent islands 110 increasethe channel area through which the fluid can flow, resulting in areduced fluidic resistance. As fluid propagates through the device 100and arrives at a gap 114, a portion of the fluid will flow into the gap114 and subsequently into the second microfluidic channel 106 (i.e., thefluid portion is extracted into channel 106). The decrease in fluidicresistance also can occur as a result of the increasing channel width inthe second microfluidic channel 106. In particular, the secondmicrofluidic channel wall 112 is slanted at an angle away from theislands so that the width of the second microfluidic channel 106increases along the channel's longitudinal direction (i.e., in thedirection of fluid propagation or the positive z-direction), thuscausing a decrease in fluidic resistance. Any increase in thecross-sectional area of the channel 106 along the longitudinal directionof the first microfluidic channel, not just an increase in width, alsocan be employed to reduce the fluidic resistance. Alternatively, or inaddition, the fluid may experience an increase in fluidic resistance inchannel 108 relative to the fluidic resistance of channel 106 (e.g.,through a decrease in the cross-sectional area of the channel 108 alongthe longitudinal direction). Thus, it may be said that the fluid isextracted in response to a change in the relative fluidic resistancebetween the second and first microfluidic channels. The change in therelative fluidic resistance may occur over the entire particle sortingregion or over a portion of the sorting region that is less than theentire particle sorting region. The change in the relative fluidicresistance may occur over along the direction of the fluid flow throughthe particle sorting region (e.g., along a longitudinal direction of theparticle sorting region as shown in FIG. 1).

With progressively lower fluidic resistance at the gaps 114 and/or inchannel 106, greater amounts of fluid flow into the second microfluidicchannel 106. Furthermore, the repeated shifting of fluid into the secondchannel 106 reduces the amount of fluid in the first channel 108. Thisconstant fluid extraction thus increases the particle-to-fluidconcentration in the first channel 108, while decreasing theconcentration of particles in the second microfluidic channel 106, suchthat the fluid in the second microfluidic channel 106 is “filtered” or“purified.” In some implementations, the particle shifting techniquesdisclosed herein may be capable of increasing the particle concentrationfrom an initial fluid sample by up to 10, 25, 50, 75, 100, 200, 300,400, or 500 times the initial particle to fluid concentration. Suchconcentration increases can result in particle yields from fluid samplesof up to 90%, up to 95%, up to 99% or even 100%.

In some implementations, the increases in particle concentrations may beachieved using multiple microfluidic devices configured to employ theparticle shifting techniques disclosed herein. For example, the outputof a first microfluidic device configured to increase the particleconcentration of an incoming fluid sample by 10× may be coupled to aninput of a second microfluidic device configured to increase theparticle concentration of an incoming fluid sample by 50×, for anoverall increase in particles concentration from the initial fluidsample of 500×.

In addition to increasing particle concentration, the repeated particleshifting may also be used to focus the particles along one or moredesired positions/streamlines within the fluid propagating through thelower channel 108. For instance, as previously explained, portions offluid may be extracted from an initial microfluidic channel into one ormore parallel microfluidic channels. In some instances, the parallelmicrofluidic channels containing the extracted fluid then may bere-combined with the initial microfluidic channel downstream so that theparticles are confined to designated streamlines in a single channel. Anadvantage of this technique of combining fluid shifting with inertiallift force is that particles may be focused to desired positions withinthe downstream channel (e.g., near the channel wall, at the middle ofthe channel, or halfway between the channel wall and the middle of thechannel, among other positions) by controlling how much fluid is removedfrom each side of the initial channel, providing increased flexibilityto the design and use of microfluidic devices. In contrast, formicrofluidic systems based primarily on inertial focusing, one cannotchoose the position of the focused stream within the channel.

The resulting concentrated and focused particle streamline may becoupled to a separate processing region of the microfluidic device 100or removed from the device 100 for additional processing and/oranalysis. Likewise, the “filtered” fluid in the second channel 106 maybe coupled to a separate region of the microfluidic device 100 orremoved from the device 100 for additional processing and/or analysis.In some implementations, the particles 102 entering the device 100 are“pre-focused” to a desired fluid streamline position that is alignedwith the first microfluidic channel 108. By pre-focusing the particles102 to a desired position, the probability that particles inadvertentlyenter into the second microfluidic channel 106 can be reduced.

Other microfluidic device configurations different from theimplementation shown in FIG. 1 also may be used to concentrate particlesbased on repeated particle and fluid shifting. For example, FIG. 2 is aschematic that illustrates an example of a device 200 for particle andfluid shifting, in which the particle shifting area includes twodifferent microfluidic channels for extracting fluid, rather than onemicrofluidic channel. The device 200 includes an inlet microfluidicchannel 204 that is fluidly coupled to a particle shifting region thathas three different fluid flow regions (an second microfluidic channel206, a first microfluidic channel 208, and a third microfluidic channel210). The second microfluidic channel 206 is separated from the firstmicrofluidic channel 208 by a first array 212 of islands 216. The thirdmicrofluidic channel 210 is separated from the first microfluidicchannel 208 by a second array 214 of islands 216. Each adjacent islandin the first array 212 and each adjacent island in the second array 214is separated by a gap for fluid shifting. The boundaries of themicrofluidic channels are defined by the device walls 218 and the wallsof the islands. The microfluidic channel walls 218 are slanted at anglesaway from the islands so that the widths of the second and thirdmicrofluidic channels (206, 210) increase along the fluid propagationdirection (i.e., the positive z-direction), thus causing a decrease influidic resistance in each channel.

The device 200 operates in a similar manner to the device 100. Inparticular, as fluid propagates substantially along the z-direction fromthe inlet channel 204 to the channels (206, 208, 210), particles 202within the fluid experience inertial lift forces in the “particle shift”regions upon approaching the walls of the inlet channel 204 and thewalls of the island structures 216. The inertial lift forces in theinlet channel 204 push the particles 202 toward the center of the fluidflow (i.e., the inertial lift forces “focus” the particles towardcentral fluid streamlines), such that they primarily flow into the firstmicrofluidic channel 208. Once the particles 202 enter the firstmicrofluidic channel 208, they experience inertial lift forces from theisland structures 216 that continue to focus the particles 202 along oneor more central streamlines extending through the channel 208. At thesame time, fluid is extracted into the second and third microfluidicchannels (206, 210) in the “fluid shift” regions due to the reducedfluidic resistance. The combination of the fluid shift regions and theparticle shift regions serve to focus particles from the incoming fluidinto the first channel 208, while increasing the concentration of theparticles at the same time. Any of the resulting fluid streams (from thesecond, first, or third channels) may be coupled to a separate region ofthe microfluidic device 200 or removed from the device 200 foradditional processing or analysis. In some implementations, thevariation in size/fluidic resistance of the second and third channelscan be set so as to ensure that equal amounts of fluid flow in from thethird channel and out the second channel at each unit.

In some cases, particle and fluid shifting can be used to createmultiple different streams of focused/concentrated particles. Forinstance, FIG. 3 is a schematic of a device 300 in which particleshifting concentrates particles from one stream along two differentmicrofluidic channels. The device 300 includes an inlet microfluidicchannel 304 that is fluidly coupled to two different fluid flow regions(a second microfluidic channel 306 and a third microfluidic channel310). A single island structure 312 positioned at the coupling pointbetween the inlet channel 404 and the second and third channels (306,310) splits fluid propagating from the inlet channel 304 into twostreams: one propagating along the second channel 306 and onepropagating along the third channel 310. Downstream from the firstisland structure 312, the second microfluidic channel 306 is separatedfrom the third microfluidic channel 310 by both a first array 314 ofislands 318 and a second array 316 of islands 318. Each adjacent islandin the first array 314 and each adjacent island in the second array 316is separated by a gap for fluid shifting.

During operation of the device 300, a fluid containing particles 302enters from the inlet channel 304. The fluid is separated by island 312causing the fluid and the particles within the fluid to flow into eitherthe second microfluidic channel 306 or the third microfluidic channel310. Once the particles 302 have entered the second and third channels(306, 310), the particles remain concentrated within those channels dueto repeated particle shifting (e.g., as a result of inertial liftforces) that occurs when the particles 302 approach the islands 318. Afirst microfluidic channel 308 is used to repeatedly extract fluid fromthe second and third channels (306, 310). In particular, the firstchannel 308 progressively increases in width, resulting in a lowerfluidic resistance. Fluid is extracted from the second and thirdchannels (306, 310) at the gaps between the islands 318 and follows thispath of lower resistance. The device 300 thus takes a fluid containingrandomly distributed particles and focuses/concentrates those particlesinto two separate streamlines in the second and third microfluidicchannels 306, 310. The resulting particle streamlines and may be coupledto separate outputs for additional processing or analysis.

The particle and shifting techniques described herein also may be usedto shift particles from a first fluid to a second different fluid, wherethe concentration of the particles in the second fluid can be increased.FIG. 4 is a schematic that illustrates an example of a device 400capable of shifting particles from one carrier fluid to another. Thedevice 400 that includes two inlet microfluidic channels (404, 406)coupled to a single microfluidic channel 405 for merging the fluids. Themerging channel 405 is, in turn, coupled to a particle shifting areathat includes two different flow regions (second microfluidic channel408 and first microfluidic channel 410). The second microfluidic channel408 is separated from the first microfluidic channel 410 by an array ofisland structures 412, in which each island 412 is separated from anadjacent island 412 by a gap 414 for fluid shifting. In addition, thetop wall 416 of the second microfluidic channel 408 is slanted at anangle away from the islands 412 in order to decrease the fluidicresistance between the second and first microfluidic channels along thedownstream fluid direction.

During operation of the device 400, a first fluid (“Fluid 1”) containingparticles 402 is introduced in the first inlet channel 404 and a secondfluid (“Fluid 2”) having no particles is introduced into the secondinlet channel 406. Assuming the fluids are introduced at flow ratescorresponding to low Reynolds numbers (and thus laminar flow), there islittle mixing between the two different fluids in the merge region 405,i.e., the two fluids essentially continue flowing as layers adjacent toone another. The fluid pathway within the merge region 405 is alignedwith the fluid pathway of the first microfluidic channel 410 such thatthe merged fluids primarily flow into the first channel 410. As the twofluids enter the first microfluidic channel 410, the particles 402within the first fluid experience inertial lift forces from the islandstructures 412 that are transverse to the direction of flow and thatkeep the particles 402 within the first microfluidic channel.

At the same time, the increasing width of the second microfluidicchannel 408 (due to the slanted channel wall 416) decreases the fluidicresistance in the openings 414 between the channels, such that portionsof the first fluid are extracted into the second channel 408 at each gapbetween the islands 412. Because the first fluid flows as a layer abovethe second fluid, it is primarily the first fluid that is extracted intothe second channel 408 from the first channel 410. After propagating fora sufficient distance past the islands 412, most of the first fluid isextracted into the second channel 408, whereas the particles 402 andmost of the second fluid remain in the first channel 410. Accordingly,the microfluidic device configuration shown in FIG. 4 is useful fortransferring particles from one fluid to a second different fluid. Insome implementations, the propagation distance is long enough so thatthe second fluid also is extracted into the second microfluidic channel408. In that case, the concentration of the particles 402 in the firstmicrofluidic channel 410 can be increased. Although the implementationshown in FIG. 4 includes two inlet channels, additional inlet channelsmay be coupled to the microfluidic channels used for altering theparticle concentration.

The microfluidic devices shown in FIGS. 1-4 implement particle shiftingacross fluid streamlines using inertial lift forces from themicrofluidic channel walls and from the periodic arrays of islandstructures. Techniques other than inertial lift force may be used toshift particles across fluid streamlines. For example, internalrepulsive forces arising due to bumping against the island structures,high Dean flow and/or high Stokes flow, such as inertial focusing, canbe used to shift particles across fluid streamlines. Alternatively, orin addition, external forces such as magnetic forces, acoustic forces,gravitational/centrifugal forces, and/or electrical forces may be usedto shift particles across fluid streamlines.

Additionally, the shape of the rigid island structures that separatedifferent flow regions is not limited to the shapes shown in FIGS. 1-4.For example, the rigid island structures may have shapes similar toposts, cuboids, or other polyhedrons in which the top and bottom facesare, or can be, congruent polygons. In some circumstances, such as athigh flow rates, it is advantageous to use islands with streamlined,tapered ends (such as the shape of the island structures in FIGS. 1-4),as the taper helps minimize the formation of flow re-circulations(eddies) that disrupt flow in unpredictable and undesirable ways. Othershapes for the rigid island structures are also possible. The long axisof the rigid island structures may be oriented at an angle with respectto the average flow direction of the fluid, the average flow directionof the particles, or the long axis of the region for altering theparticle concentration. The shapes of the channel segments are notlimited to the approximately rectangular shapes shown in FIGS. 1-4. Thechannel segments may include curves or substantial changes in width. Incross-section, the channels described in FIGS. 1-4 may be square,rectangular, trapezoidal, or rounded. Other shapes for the channelcross-sections are also possible. The channel depth may be uniformacross the region for altering the particle concentration, or thechannel depth may vary laterally or longitudinally. Additionally, thoughFIGS. 1-4 show the microfluidic channels as approximately rectilinearpathways, the channels may be configured in other differentarrangements. For example, in some implementations, the microfluidicchannels may be formed to have a spiral configuration. For instance, thefirst microfluidic channel and the second microfluidic channel may bearranged in a spiral configuration, in which the first and secondmicrofluidic channel are still be separated by the array of islandstructures, but where the longitudinal direction of fluid flow throughthe channels would follow a generally spiral pathway.

In some implementations, the microfluidic devices can be designed toincorporate redundancy so as to prevent particles that unintentionallypass with fluid through openings in a first array of island structuresfrom ultimately being collected with the filtered fluid. For example, insome cases, the devices may be designed to include two or more“confinement channels” operating in parallel, i.e., two or morechannels, such as channel 108 in FIG. 1, that are designed to impartrepulsive forces to substantially prevent particles from passing throughopenings in the island array. Since particles would need to overcome therepulsive forces associated with each additional channel, theprobability of a particle escaping with fluid that passes throughopenings between islands decreases as more confinement channels areadded.

In some implementations, the devices described herein may be used inconjunction with other microfluidic modules for manipulating fluidsand/or particles including, for example, filters for filteringsub-populations of particles of certain sizes. In addition, the devicesdescribed herein may be used in series and/or in parallel within amicrofluidic system.

Altering Particle Concentration/Reducing Fluid Volume Using InertialFocusing and Fluid Shifting

Altering the concentration of particles within microfluidic samples isnot limited to techniques that rely on a combination of fluid shiftingwith inertial lift forces and/or bumping forces to direct particlesacross fluid streamlines. Other internal forces, such as inertialfocusing or viscoelastic focusing may be used in combination with fluidshifting as well.

With respect to inertial focusing, an inherent advantage is that thefluid forces depend on higher speed flows rather than low Reynoldsnumber operation, thus leading to higher throughput, which is otherwisea common limitation of microfluidic devices.

Inertial focusing uses inertial forces to enable the precise lateralpositioning of particles within a microfluidic channel, e.g., along acommon streamline. Inertial focusing is based upon the notion thatlaminar flow of a fluid through microfluidic channels can result in thecontinuous and accurate self-ordering of particles suspended within thefluid from a randomly distributed state. In general, sorting, ordering,and focusing of particles in an inertial focusing system depends, interalia, on the geometry of the microfluidic channel, the ratio of particlesize to hydrodynamic cross-sectional size of the channel, and the speedof the fluid flow. Various channel geometries may require apredetermined particle-to-volume ratio of the particle to be focused toachieve a desired inter-particle spacing and thereby maintain orderingand focusing of those particles.

In general, a maximum particle-to-volume ratio for a specified particlesize and channel geometry for inertial focusing alone can be determinedusing the formula:

${MaxVolumeFraction} = \frac{2N\pi a^{2}}{3hw}$

where N is the number of focusing positions in a channel, a is theaverage focused particle diameter, h is the microfluidic channel height,and w is the channel width. Higher ratios may be achieved whenadditional forces are applied to the particles.

Different microfluidic channel geometries can be used to achieveinertial focusing of particles. For example, the microfluidic channelcan be a symmetrically curved channel, such as S-shaped, sinusoidal, orsigmoidal. The channel can have various cross-sections, such as arectangular, elliptical, or circular cross-section. Alternatively, thechannel can be an asymmetrically curved channel having various shapes,cross-sections, and configurations as needed for a particularapplication (e.g., each curve in the channel can be a different size,or, for example, the odd-numbered curves in a channel may be a firstsize and shape and the even-numbered curves may be a second size andshape, or vice versa). For example, the channel can generally have theshape of a wave having large and small turns, where a radius ofcurvature can change after each inflection point of the wave. Themaximum particle-to-volume ratio can be adjusted as necessary for theparticular geometry.

The channel can be configured to focus particles within a fluid sampleinto one or more discrete streamlines at one or more equilibriumpositions within the channel. In general, separation, ordering, andfocusing are primarily controlled by a ratio of particle size to channelsize and the flow characteristics of the system, but is independent ofparticle density. For example, analytes can have a hydrodynamic sizethat is in the range of about 1000 microns to about 0.01 microns. Moreparticularly, analytes can have a hydrodynamic size that is in the rangeof about 500 microns to about 0.1 micron, such as between about 100microns and about 1 micron. In general, the analyte size is limited bychannel geometry. Analytes that are both larger and smaller than theabove-described ranges can be ordered and focused within inertialfocusing regions having laminar flow conditions.

Lateral migration of particles in shear flow arises from the presence ofinertial lift, attributed mainly to the shear-gradient-induced inertia(lift in an unbounded parabolic flow) that is directed down the sheargradient toward the wall, and the wall induced inertia which pushesparticles away from the wall. Particles suspended in fluids aresubjected to drag and lift forces that scale independently with thefluid dynamic parameters of the system. Two dimensionless Reynoldsnumbers can be defined to describe the flow of particles in closedchannel systems: the channel Reynolds number (R_(c)), which describesthe unperturbed channel flow, and the particle Reynolds number (R_(p)),which includes parameters describing both the particle and the channelthrough which it is translating:

$R_{c} = \frac{U_{m}D_{h}}{v}$ and$R_{p} = {{R_{c}\frac{a^{2}}{D_{h}^{2}}} = {\frac{U_{m}a^{2}}{vD_{h}}.}}$

Both dimensionless groups depend on the maximum channel velocity, U_(m),the kinematic viscosity of the fluid, and ν=μ/ρ (μ and ρ being thedynamic viscosity and density of the fluid, respectively), and D_(h) thehydraulic diameter, defined as 2wh/(w+h) (w and h being the width andheight of the channel, respectively, for a channel having a rectangularor square cross-section). The particle Reynolds number has an additionaldependence on the particle diameter a. The definition of Reynolds numberbased on the mean channel velocity can be related to R_(c) by R_(e)=⅔R_(c). Inertial lift forces dominate particle behavior when the particleReynolds number, R_(p), is of order 1. Typically, particle flow inmicroscale channels is dominated by viscous interactions with R_(p)«1.In these systems, particles are accelerated to the local fluid velocitybecause of viscous drag of the fluid over the particle surface. Dilutesuspensions of neutrally buoyant particles are not observed to migrateacross streamlines, resulting in the same distribution seen at theinlet, along the length, and at the outlet of a channel. As R_(p)increases, migration across streamlines occurs in macro scale systems.An example of R_(p) that allows localization of a flux of cells from ablood sample within a rectangular or square channel is about 2.9, butthis can range from about 0.02 to 2.9 or higher. Again, differentmicrofluidic channel geometries can be used to achieve inertial focusingof particles, resulting in corresponding Reynolds numbers suitable forthose channel geometries. Examples and further discussion of inertialfocusing can be found, for example, in U.S. Pat. No. 8,186,913, which isincorporated herein by reference in its entirety.

Generally, inertial focusing is used to focus particles to one or moreequilibrium positions and then flow the different focused streams ofparticles to distinct outputs, where the particles are then collected.However, by adding the repetitive removal of fluid from the focusedstream, the ability of inertial focusing to substantially increaseparticle concentration within a fluid (and/or reduce the concentrationof particles in a fluid sample) may be greatly improved. In particular,the technique relies on two different behaviors that enable asubstantial and rapid reduction in fluid volume: 1) a fast depletion ofthe near wall regions and 2) a reduced shear gradient lift drivenmigration of particles to their equilibrium positions.

FIG. 5 is a schematic illustrating a top view of an example of aparticle shifting area 500 of a microfluidic device, in which theparticle shifting area 500 relies on inertial focusing in combinationwith repeated fluid extraction to enhance volume reduction from aparticle-rich fluid sample. Fluid samples may be provided to particleshifting area 500 using, e.g., pumps, in a manner similar to thatdescribed with respect to other embodiments disclosed herein. Theparticle shifting area 500 includes an array of island structures 504separating an elongated second fluid flow region 506 from an elongatedfirst fluid flow region 508. The first fluid flow region 508 may also becalled the “focusing channel” and the second fluid flow region 506 maybe called the “particle-free channel.” In the present example a particlecontaining fluid sample is introduced into flow region 508, whereas, aparticle-free fluid sample, which may be the same or different fluid asthat propagating in region 508, is introduced into flow region 506.

Each island 504 is separated from an adjacent island 504 in the array bya corresponding gap 510 that allows fluid to cross between the secondand first flow regions. In contrast to the devices shown in FIGS. 1-4,the first flow region 508 has an undulating channel wall 512 (e.g.,approximately sinusoidal in shape) in which the channel width (along they-direction in FIG. 5) alternates between being narrow and enlargedalong the longitudinal direction (along the z-direction in FIG. 5).Additionally, each island structure 504 has a curved contour thatfollows the curvature of portions of the peaks and troughs in thechannel wall 512. That is, a side of each island and an opposing side ofthe second channel have substantially matching contours. In the presentexample, this leads to flow region 508 having an undulating longitudinalpathway through which the particle-carrying fluid sample propagates.

More specifically, a first turn through flow region 508 is narrow andthe matching contours of the wall 512 and island 504 have small radii ofcurvature, whereas a second adjacent turn through flow region 508 iswider and the matching contours of the wall 512 and island have largerradii of curvature. This pattern of a relatively small radius ofcurvature followed by a relatively larger radius of curvature isrepeated over the length of the flow region 508. Thus, the microfluidicchannel is asymmetrically curved to create higher fluid speeds closer tothe wall 512 than away from the wall 512. Depending on the flow rate ofa particle carrying fluid, the fluid pathway curvature of the first flowregion 508 may generate inertial forces that focus and retain particles502 along one or more fluid streamlines within the first flow region508.

Additionally, the fluidic resistance near the gaps 510 between islands504 decreases so that a portion of fluid tends to follow the lowresistance path and shift/flow into the second flow region 506. Thisfluid flow also tends to pull particles 502 traveling with fluid in thedirection of the gaps 510. However, in certain implementations, theinertial forces generated by the undulating fluid pathway of this regionare great enough to shift the particle 502 across fluid streamlines andaway from the gaps 510 so that the particle 502 remains suspended in theportion of fluid traveling through the first flow region 508. The secondfluid flow region 506 can be configured to have a width thatprogressively increases so the fluidic resistance in that regiondecreases over the channel length. As a result, greater amounts ofparticle-free fluid will shift into the second fluid flow region fartherdownstream along the channel, and lead to an increase in particleconcentration in the first fluid flow region 508.

FIG. 6A is a schematic depicting how fluid streamlines may behave withina microfluidic device 600 that combines inertial focusing with repeatedfluid extraction. The structure of the device shown in FIG. 6A issimilar to the device 500 and includes an input region 601, where afluid suspension containing a dilute concentration of particles (e.g.,cells) is introduced. As the dilute sample of particles enters thedevice, the fluid sample is accelerated when the microfluidic channelconverges toward a first narrow neck region 603. A particle-free layer(labeled “cell free layer” in FIG. 6) 605 forms after the fluid samplepasses through the neck region 603 as a result of the cells moving awayfrom the wall by Dean flow. A portion of this particle-free layer 605then passes/is siphoned off toward the second fluid flow region 606 atthe first island structure 612, whereas the particles remain in thefirst fluid flow region 608. The amount of the fluid sample that passesinto the second fluid flow region 606 depends on the hydraulicresistance of the openings and the second fluid flow region 606 relativeto the hydraulic resistance of the first fluid flow region 608. Theprocess of accelerating the particle-rich fluid to create aparticle-free layer, and passing the particle-free layer into the secondfluid flow region 606 is repeated multiple times at each island 612until the end of the device where the separate flows may be captured forfurther processing or removal from the device. For instance, the device600 may be understood as having a repeating array of focusing units andsiphoning units arranged in parallel (i.e., a “focusing-siphoning unitpair”). An example of the regions corresponding to a single focusingunit 607 and a single siphoning unit 609 are depicted in FIG. 6A. Thefocusing unit 607 includes the area adjacent to an island structure 612where the walls of the microfluidic channel have relatively highcurvature to induce inertial focusing. The siphoning unit 609 includesthe area adjacent to the same island structure, but opposite to that ofthe focusing unit 607, that has relatively less curvature and whichprovides a wider pathway for fluid to travel, resulting in a lowerhydraulic resistance. In the example shown in FIG. 6, the width of eachsiphoning unit 609 (as determined along a direction transverse to fluidflow) increases along the direction of fluid flow, leading to lowerfluidic resistance and therefore an increase in the amount of fluidpassing from the first fluid flow region 608.

FIG. 6B includes plots of simulated fluid flow for differentcross-sections of the device 600 shown in FIG. 6A. The plots in FIG. 6Bdepict the Dean flow vectors and velocity profile which causes theformation of the cell free layer. As can be seen from these plots, theoverall flow speed, and thus the inertial force, of the fluid sampledecreases along the length of the microfluidic channel as fluid passesinto the second fluid flow region 606. In other words, to achieve agiven level of volume reduction, the flow speed must be reduced to afixed degree, independent of the number of units used.

An important design consideration for a device that combines inertialfocusing with repeated fluid extraction is the percentage of the fluidthat is siphoned at each siphoning unit. Ideally, the greater the amountof particle-free fluid that is removed at each siphoning unit, thequicker one will be able to obtain a desired particle concentration inthe particle-rich fluid. However, it is also the case that the higherthe percentage of fluid that is siphoned, the greater is the risk thatparticles will be carried away with the siphoned fluid if the inertialforces do not shift the cells out of the larger siphoned fluid fraction.

FIG. 7 is a plot that depicts the results of a calculation based on thedevice structure shown in FIG. 6B. The calculation was performed todetermine the Cell Free Flow Fraction as a function of the number ofsiphon-focusing unit pairs and the percentage of fluid that passes intothe particle-free layer at each opening between the island structures ofthe device. “Cell Free Flow Fraction” refers to the fraction of allfluid that has been siphoned out. For example, if the siphon percentageis 10%, then after one unit the cell free flow fraction is 10%. Theother 90% remains in focusing units. Then, in the second unit remove 10%of the remaining 90% is removed (i.e., 9% of the overall fluid). Thus,after two units the Cell Free Flow Fraction is 19%. This continues on.The plot also includes two horizontal dashed lines, with the top linerepresenting a factor of 50 times reduction in fluid volume of theparticle-rich fluid, and the bottom dashed line representing a factor of10 times reduction in fluid volume of the particle-rich fluid. The fourdifferent curves in FIG. 7 represent siphoning at four differentpercentages, with the smallest siphon percentage corresponding to thebottom curve and the highest siphon percentage corresponding to the topcurve in the plot. As shown in FIG. 7, higher siphon percentages (i.e.,the percentage of fluid siphoned at each siphon unit) decrease theoverall number of units required to reach an equivalent volume reductionfactor seen at the intersections of the 10× and 50× dashed lines.

A microfluidic device that combines inertial focusing and siphoning isnot limited to the configuration shown in FIG. 5. For example, in someimplementations, a combined inertial focusing and siphoning device mayhave a configuration that includes an second fluid flow channel, a first(center) fluid flow channel and a third fluid flow channel similar tothe device shown in FIG. 2, with the exception that the device would beconstructed to induce inertial focusing in the center channel. Forexample, the center channel may be configured to have an undulatingpathway/shape in which the channel width (as determined transverse tothe direction of fluid flow) alternates between narrow and enlarged.This may be achieved by constructing each of the first and second arrayof island structures to have matching contours that alternate betweenregions of high and low curvature. As in the example of FIG. 2, fluidpasses into the second and third channels at the openings/gaps betweenthe island structures. Alternatively, in some implementations, thedevice can be constructed to induce inertial focusing in the second andthird fluid flow channels. For example, each of the second and thirdfluid flow channels may be configured to have an undulatingpathway/shape in which their widths alternate between narrow andenlarged. This may be achieved by constructing the walls of the secondchannel and the opposing array of island structures to have matchingcontours that alternate between regions of high and low curvature,whereas the walls of the third channel and an opposing array of islandstructures may also have matching contours that alternate betweenregions of high and low curvature. At the gaps/openings between theisland structures in each array, fluid may pass from the second channelinto the center channel and from the third channel into the centerchannel.

In some implementations, the combined inertial focusing and siphoningdevice may have two fluid inputs, similar to the device 400 shown inFIG. 4, so that the device acts as a fluid exchanger, where particlesare transferred from a first fluid to a second fluid. That is, a firstfluid sample may be introduced through input 406, whereas a seconddifferent fluid sample containing particles 402 may be introduced intoinput 404. Initially, a portion of the second fluid sample containingthe particles 402 and first fluid sample propagate side by side throughchannel 410. The walls of the first channel 410 and the islandstructures 412 may be configured so that the first channel 410 has anundulating pathway/shape in which the width of the channel alternatesbetween narrow and enlarged (similar to the configuration shown in FIG.5). The undulating channel 410 leads to focusing of the particles alongstreamlines within the first fluid sample in channel 410.Simultaneously, portions of the second fluid sample that are free ofparticles 402 are extracted from channel 410 at the gaps 414 betweenislands 412 into the second channel 408. After repeated extraction ofthe second fluid sample, the particles 402 eventually are entirelytransferred to the first fluid sample within channel 410, and the secondfluid sample is particle free.

In some implementations, a microfluidic device includes a particleshifting area having multiple channels that rely on inertial focusing incombination with repeated fluid extraction. Using multiple channelsallows, in some implementations, a substantial increase in thethroughput of a microfluidic device. For example, multiple copies of theparticle shifting area 500 shown in FIG. 5 may be arranged in parallel.The output of each of the channels containing the particles may bedelivered to a common repository. Similarly, the output of each of thechannels containing the particle-free fluid also may be delivered to adifferent common repository.

In contrast to conventional centrifugation, an advantage of devices thatuse the combined inertial focusing and siphoning techniques is thatparticles are exposed to heightened forces for a shorter duration (e.g.,fractions of seconds) than during centrifugation (e.g., severalminutes). Additionally, compaction of particles does not occur in themicrofluidic volume reduction process. Cell compaction, which may occurin centrifugation processes, is known to mechanically damage certaincells as well as alter gene expression (see, e.g., Peterson, B. W.,Sharma, P. K., Van Der Mei, H. C. & Busscher, H. J. “Bacterial CellSurface Damage Due to Centrifugal Compaction,” Applied and EnvironmentalMicrobiology 78, 120-125 (2012), incorporated herein by reference in itsentirety). Additionally, the short duration over which cells may beexposed to heightened forces in a combined siphoning and inertialfocusing device results in little or no restructuring of cells'interiors. In contrast, centrifugation techniques are susceptible tocausing the dislocation of organelles. Moreover, there is no need forsterile breaks between steps in the combined siphoning and inertialfocusing devices, unlike when transferring samples from a centrifuge.Thus, compared to centrifugation, the combined siphoning and inertialfocusing devices offer a more efficient closed system for performingcommon biomedical tasks.

Increasing Particle Concentration/Reducing Fluid Volume UsingViscoelastic Focusing

As explained above, viscoelastic focusing also may be used incombination with fluid shifting to alter the concentration of particleswithin a fluid sample. In some implementations, viscoelastic focusingincludes the addition of specified concentrations (e.g., micromolarconcentrations or other concentrations) of one or more drag-reducingpolymers (e.g., hyaluronic acid (HA)) to a fluid that results in a fluidviscoelasticity that can be used to control the focal position of theparticles within the moving fluid at different Reynolds numbers (Re).

With viscoelastic focusing, the volumetric flow rate at which aparticle-carrying fluid is driven results in the formation of alocalized streamline in the fluid at or near a center of the channel.The localized streamline defines a width that is substantially equal toor slightly greater than a hydraulic diameter of a particle within thefluid. By adding the drag-reducing polymer to a Newtonian fluid (e.g.,water or a physiological saline solution), the particle in the fluid isfocused into the localized streamline, creating particle-free regions atthe edges of the channel (e.g., the regions closest to the channelboundaries or walls).

Thus, similar to inertial focusing, viscoelastic focusing enables theprecise positioning of particles within a fluid along a commonstreamline. In contrast to inertial focusing, viscoelastic focusing hasan equilibrium position at the center of the channel cross-section,i.e., along a longitudinal path extending in a direction of fluid flowand centered between walls of the channel. Viscoelastic focusing alsoworks across large ranges of flow rates and Reynolds numbers. Thetechnique of viscoelastic focusing thus can be coupled with fluidextraction as described herein (e.g., repetitive removal/siphoning offluid from the focused stream) to substantially alter particleconcentration within a fluid.

Any of the devices described herein may be used with viscoelasticfocusing to focus particles to a streamline within a fluid and alter theparticles' concentration within the fluid. For example, viscoelasticfocusing may be used with the device 200 shown in FIG. 2. A pump (notshown) connected to the inlet of channels 206 and 210 may be operated todrive a fluid that carries suspended particles 202. In someimplementations, the pump is operated to drive the fluid through thechannels at volumetric flow rates that result in the formation of alocalized streamline in the fluid at or near a center of the centerchannel 208, e.g., defined by the axis 220. The localized streamline 220defines a width that is substantially equal to or greater than ahydraulic diameter of the particle 202. The particles in the fluid arefocused into the localized streamline 220. The localized streamline 220represents a portion of the fluid into which the suspended particles 202are focused. That is, the suspended particles are focused into astreamline formed by the fluid flow at or near a center of the channel208. At the same time, fluid may be extracted at the gaps/openingsbetween the islands 212, 214 that separate the second and third channels206, 210 from the center channel 208. Because the particles are focusedto a center streamline, the particles 202 are located further away fromthe gaps between islands and are less likely to be carried out of thecenter channel 208 with the portions of the fluid sample being extractedinto the second and third channels 206, 210. That is, at each gap aportion of particle-free fluid is extracted from the center channel 208into either channel 206 or channel 210, resulting in an increase in theconcentration of particles within the center channel 208. After repeatedsiphoning of fluid at the gaps, the concentration of the particles maybe increased, e.g., from 10 to 100 times or more.

The fluid in which the particles 202 are suspended and which is flowedthrough the channels 206, 208, 210 can include a Newtonian fluid, e.g.,water or other Newtonian fluid, or a drag-reducing polymer mixed with aNewtonian fluid. In general, any polymer (or material) that can decreasea drag on particles, e.g., by exerting viscoelastic normal stresses onthe particles, at the volumetric flow rates described herein can beimplemented as an alternative or in addition to HA. In other words, anymaterial (e.g., polymer, or other material) which, when mixed with aNewtonian fluid, alters a drag on a particle suspended in thefluid-material mixture, relative to a drag on the particle suspended inthe Newtonian fluid without the material can be implemented as analternative or in addition to HA. Such materials can include, e.g.,polyethylene oxide (PEO), polyacrylamide, gelatin, to name a few. Theparticles can include rigid particles, e.g., beads, or deformableparticles. In some implementations, the particles can include biologicalparticles, e.g., cells. The drag-reducing polymer can include hyaluronicacid (HA). The molecular weight of HA can be between 350 kDa and 1650kDa. The Reynolds number of the fluid flow can be between 0.001 and4500, e.g., between 0.01 and 20, between 0.01 and 15, between 0.01 and10, between 0.01 and 1, between 0.1 and 1000, between 0.1 and 100,between 0.1 and 20, between 0.1 and 10, between 0.1 and 1, between 1 and1000, between 1 and 100, or between 1 and 20. The concentration of thedrag-reducing polymer can be between about 0.001-1% g/mL (0.00001-0.01g/mL) such as between about 0.01-0.1% g/mL (0.0001-0.001 g/mL). Furtherdiscussion of viscoelastic focusing can be found, e.g., in WO2015/116990, which is incorporated herein by reference in its entirety.

Microfluidic Device Design Parameters

The effect of various design parameters on the operation of themicrofluidic device will now be described. For reference, FIG. 16 is aschematic illustrating a top view of an example particle and fluidshifting region 1600 containing a row of island structures 1610. The rowof island structures 1610 separates an “extraction” microfluidic channel1605 from a “particle” microfluidic channel 1607. The primary directionof fluid flow is indicated by the arrow 1601. The width of theextraction channel 1605 (defined along the y-direction) expands alongthe length of the channel, whereas the width of the particle channel1607 (defined along the y-direction) remains essentially constant alongthe length of the channel. During operation of the device, fluid isextracted into the extraction channel 1605 through the openings betweenthe islands 1610, while particles traveling within the particle channel1607 are retained in the particle channel 1607 by repulsive forces,e.g., inertial lift forces. For the purposes of the followingdiscussion, the channels and islands may be understood as being arrangedinto separate “units” (see Unit 1, Unit 2 and Unit 3 in FIG. 16).Specifically, FIG. 16 illustrates three units of an array with each unitincluding a portion of the exterior microfluidic channel 1605, an island1610, and a portion of the particle channel 1607.

The relevant design parameters for the particle and fluid shiftingregion 1600 include the length of each unit, the width of each channel,and the fluid shift for each unit. The fluid shift, f_(s), is thefraction of the fluid flow, q, that shifts between channels at each unit(i.e., at the openings between the island structures). Together theseparameters determine the fluid conductance of the channels in each unitof the device. Thus, each unit has a particle channel with length l_(i),a particle channel width w_(p,i), and a particle channel fluidicconductance g_(p,i), where i refers to the unit number. Each unit alsohas an extraction fluid channel with length l_(i), an extraction channelwidth w_(e,i), and an extraction channel fluidic conductance g_(e,i),where i refers to the unit number. In the example described here, allchannels are rectangular in shape and the fluid shift is the same foreach unit. The basic method presented here can be easily modified fornon-rectangular (e.g., curving) channels and varying shift.

At each unit, the total flow divides between the particle and extractionfluid channels in proportion to their relative fluidic conductances.Thus, the fraction of the total flow that flows through the particlechannel 1607 in the i^(th) unit is

$f_{p,i} = {\frac{q_{p,i}}{q_{p,i} + q_{e,i}} = \frac{g_{p,i}}{g_{p,i} + g_{e,i}}}$

where q_(p,i), and q_(e,i), are the flow rates of the particle andextraction fluid channels, respectively. Similarly, the fraction of thetotal flow that flows through the extraction fluid channel 1605 in thei^(th) unit is

$f_{e,i} = {\frac{q_{e,i}}{q_{p,i} + q_{e,i}} = \frac{g_{e,i}}{g_{p,i} + g_{e,i}}}$

The dimensions of the particle channel 1607 are chosen to optimallyshift particles across streamlines (e.g., away from the extraction fluidchannel 1605). Because the flow rate q_(p,i), changes along the lengthof the device, the particle channel dimensions may be altered tomaintain optimal particle shifting. For example, as q_(p,i), decreases,the unit length l_(i) may be increased to compensate for the weakeninginertial lift force operating on particles.

The dimensions of the extraction fluid channel 1605 are chosen toprovide a conductance g_(e,i), such that a precise fraction of the fluidin the particle channel 1607 shifts to the extracted fluid channel ateach unit. This fractional amount is called the fluid shift, f_(s). Theresult of this shifting is that the fraction of flow in the particlechannel decreases by a fixed factor at each unit:

f _(p,i)=(1−f _(s))f _(p,i-1)

For example, if f_(s)=0.1, then fraction of flow in the particle channelwill be 90% of the fraction of flow in the particle channel of theprevious unit. More generally, because f_(p,0)=1,

f _(p,i)=(1−f _(s))^(i)

Thus, for the example case shown in FIG. 16 in which the particle andfluid shifting region is divided into three units, f_(s)=0.1,f_(p,1)=0.9, f_(p,2)=0.81, and f_(p,3)=0.729.

Recall that the fraction of flow in the particle channel is alsodescribed by

$f_{p,i} = \frac{g_{p,i}}{g_{p,i} + g_{e,i}}$

Substituting for f_(p,i) and solving for g_(e,i):

g _(e,i)=((1−f _(s))^(−i)−1)g _(p,i)

Thus, for each unit the conductance of the extracted fluid channel canbe written in terms of the conductance of the particle channel and thefluid shift. The fluidic conductance, g, of each channel is a functionof its dimensions and the fluid viscosity. In the device described here,each channel is rectangular and therefore has conductance that can beexpressed as

$g \approx {\left( \frac{h^{4}}{12\eta l\alpha} \right)\left( {1 - {{0.6}3\alpha}} \right)}$

Here, η is fluid viscosity, l is channel length, w is channel width, his channel height, and α=h/w. A more accurate infinite series-basedformula is also available (Tanyeri et al., “A microfluidic-basedhydrodynamic trap: Design and implementation (Supplementary Material).”Lab on a Chip (2011).) Computational modeling or empirical methods canbe used to determine the conductance of more complex channel geometries.(Note that in this description it is simpler to focus on fluidicconductance, g, rather than fluidic resistance, R. The two quantitiesare simply related by g=1/R.)

Using the above formulas, a microfluidic device for increasing theconcentration of particles within a fluid sample may be implemented asfollows:

-   -   1. The dimensions of the particle channel are chosen for each        unit in the device. As mentioned, the dimensions are chosen to        optimally shift particles away from the extracted fluid channel.    -   2. Using these dimensions and the fluid viscosity, the particle        channel conductance g_(p,i) is determined for each unit using        the rectangular channel conductance formula (or an equivalent        method).    -   3. The extraction fluid channel conductance g_(e,i) is then        evaluated for each unit using the previously determined g_(p,i)        and f_(s). The width of the extraction fluid channel, w_(e,i),        is then chosen to give the desired g_(e,i) for each unit. In        practice, the width may be determined by evaluating fluidic        conductance (using the above formula) across a wide range of        channel widths and then interpolating to find the channel width        that gives the desired channel conductance.

For concentrators with straight channels that rely on inertial liftforces to shift particles across streamlines, the following are devicedesign and operation guidelines:

First, as described in “Inertial Microfluidics,” Di Carlo, Lab Chip (9),3038-3046, 2009 (incorporated herein by reference in its entirety), theratio of the lateral (across channel) particle velocity U_(y) to thelongitudinal (in direction of fluid flow) velocity U_(z) is proportionalto the particle Reynolds number R_(p):

${\frac{U_{y}}{U_{z}} \propto R_{p}} = \frac{U_{m}a^{2}}{vD_{h}}$

Here U_(m) is the maximum channel velocity, a is the particle diameter,v is the kinematic viscosity of the fluid, and D_(h) is the hydraulicdiameter of the channel. (For channels of rectangular cross-section withwidth w and height h, D_(h)=(2wh)/(w+h).) Because it is the aim of theparticle concentrator device described here to use inertial lift forcesto efficiently move particles across streamlines (e.g., maximizeU_(y)/U_(z)), it is recommended that the channel dimensions and flowconditions be selected so as to maximize particle Reynolds number R_(p)in the particle channel to the extent permitted by other practicalconstraints, such as operating pressure. Throughout the device, theparticle Reynolds number R_(p) in the particle channel should ideally begreater than about 0.01, though it may be much larger than this,possibly greater than 100.

For a given particle diameter a and kinematic viscosity v, a targetparticle Reynolds number R_(p) can be achieved through many differentcombinations of channel dimensions and channel velocities. One strategyfor increasing R_(p) would be to select a very small (relative to a)hydraulic diameter D_(h). However, channel resistance has a quarticdependence on D_(h), and choosing an unnecessarily small D_(h) comes atthe cost of highly increased operating pressure. On the contrary, theoperating pressure scales linearly with channel velocity U_(m), so agood alternative strategy is to design a device with a modest hydraulicdiameter D_(h) and then increase channel velocity U_(m) (and thereforeR_(p)) at the time of operation as needed to achieve high yield ofparticles. For a channel with square cross-section, such that D_(h)=w=h,a value of D_(h) approximately five times the particle diameter a is areasonable choice: D_(h)=5a.

Second, the length of the openings (in the longitudinal direction)between islands should be greater than about a and less than or equal toabout w. If the length of the opening is less than a, the opening mayclog with particles, thereby disrupting flow through the opening. Anopening with length approximately equal to w is unlikely to clog withparticles and provides adequate room for fluid to cross between islandsto the adjacent channel. An opening with a length greater than w willwork but provides no particular benefit and comes at the cost of wastedspace.

Third, the length of the islands/should be greater than or equal to thelength of the openings between islands. As aforementioned, it is the aimof the particle concentrator device to use inertial lift forces toefficiently move particles across streamlines. Because particles onlyexperience inertial lift forces as they travel alongside islands,particles should travel most of their longitudinal distance alongsideislands, rather than across openings between islands. Put another way,if the length of islands and the length of the openings between islandsare equal, then particles experience inertial lift forces along just 50%of the distance they travel. On the other hand, if the length of theislands is four times the length of the openings, then particlesexperience inertial lift forces along 80% of the distance they travel.

A loose upper limit on the length of islands/is the length required forparticles to migrate to equilibrium focusing positions. Any additionalchannel length beyond what is required for particles to reachequilibrium does not contribute to shifting particles acrossstreamlines. A formula for the channel length Lf required for particlesto reach equilibrium is given in “Inertial Microfluidics,” Di Carlo, LabChip (9), 3038-3046, 2009:

$L_{f} = \frac{\pi\mu w^{2}}{\rho U_{m}a^{2}f_{L}}$

Here μ is dynamic viscosity, w is channel width, ρ is fluid density,U_(m) is the maximum channel velocity, a is the particle diameter, andf_(L) is a dimensionless constant ranging from about 0.02 to 0.05 forchannels with aspect ratios (h/w) ranging from about 2 to 0.5. WhileL_(f) provides an upper bound, it is a loose upper bound and exceeds theoptimal length of islands l. This is because the lift force on particlesis very strong near the channel wall (proportional to a⁶), but falls offsharply with distance from the wall (proportional to a³ near the centerof the channel). Thus, a concentrator device will more efficiently shiftparticles across streamlines if the particles are kept near the channelwall by using an island length l that is significantly less than L_(f).

Given these considerations, a reasonable intermediate value for theisland length is about l=4w. This is an approximate value andnecessarily depends on the values selected for other parameters, such asthe fluid shift f_(s). It is also important to note that the length ofthe islands l need not be constant along the length of the device.Rather, as the maximum channel velocity U_(m) and particle Reynoldsnumber R_(p) in the particle channel decrease, the lengths of theislands can be increased to compensate. For example, a factor of twodecrease in R_(p) can be compensated by a factor of two increase inisland length l. Up to a point, the lateral deflection distance ofparticles per unit is expected to be roughly proportional to the islandlength l.

Fourth, the fluid shift f_(s) should be greater than 0.2% and ideallygreater than 1.0%. If the fluid shift is small, e.g., 0.1%, then thetotal number of shifts (units) needed to achieve a significant volumereduction, e.g., 10×, is very large and the device itself must thereforebe very long. Provided the maximum channel velocity U_(m) issufficiently high to place the particle Reynolds number R_(p) in theprescribed range, an extremely small shift, e.g., 0.1%, should not benecessary. Depending on the maximum channel velocity U_(m), a fluidshift f_(s) in the range of about 1% to 5% should perform well for adevice designed and operated as outlined here.

It is important to note that the fluid shift f_(s), like the length ofthe islands l, need not be constant along the length of the device.Rather, as the maximum channel velocity U_(m) and particle Reynoldsnumber R_(p) in the particle channel decrease, the fluid shift f_(s) canbe reduced to compensate. For example, a factor of two decrease in R_(p)can be compensated by a factor of two decrease in fluid shift f_(s).Either or both of these compensation strategies can be implemented tooptimize device efficiency and performance.

For any given device design and particle size a, the final parameterchoice is the device operating flow rate, which directly determines themaximum channel velocity U_(m) and the particle Reynolds number R_(p) inthe particle channel. For a device designed as outlined, there will be aminimum flow rate required for good performance. Below this thresholdflow rate, the inertial lift forces will be insufficient to shiftparticles far enough from the island wall to avoid being shifted asfluid is extracted (siphoned), thus resulting in low yield of particles.While the formulas provided here enable one to make rough estimates ofthe threshold flow rate, the most accurate and relevant method ofdetermining the threshold flow rate is empirically.

Other design and optimization strategies may also result in effective,high performance concentrator devices.

A microfluidic device that is configured to shift particles of a givensize can, in some implementations, be scaled to effectively shiftparticles of a different size. For instance, for a device that employsinertial lift forces to shift particles across fluid streamlines, onecan scale the dimensions of the particle shifting area with particlesize and alter the flow conditions, so long as the value of the particleReynolds number, R_(p), is preserved. The particle Reynolds number canbe expressed as:

$R_{p} = \frac{U_{m}a^{2}}{vD_{h}}$

where U_(m) is the maximum channel velocity, a is the particle diameter,v is the kinematic viscosity of the fluid, and D_(h) is the hydraulicdiameter of the channel. (For channels of rectangular cross-section withwidth w and height h, D_(h)=(2wh)/(w+h).) For example, consider aShifting Area 1 that effectively shifts particles of size a. One methodof designing a Shifting Area 2 that effectively shifts particles of size2a is scale all dimensions of Shifting Area 1 by a factor of 2 (i.e.,double the length, width, and height of all features). To maintain thesame R_(p) in Shifting Area 2, the maximum channel velocity U_(m) mustbe decreased by a factor of 2.

Other methods of scaling the dimensions of particle shifting areas andflow conditions with particle size are also possible.

Ease of microfluidic device manufacturing is largely determined by theaspect ratio (height divided by width) of the device structures, withsmaller aspect ratio devices being easier to manufacture at low cost andwith high manufacturing yield. We can define the aspect ratio in twoways. The minimum aspect ratio is the structure height, h, divided bythe minimum structure width, w_(min). The overall aspect ratio is thestructure height, h, divided by the diameter, D, of a circle with thesame area as the structure. Here, D=√(4A/π), where A is the area of thestructure.

As an example, for a microfluidic device having substantially straightchannels, the island structures may have a length of about 50-1000 μm, awidth of about 50 μm, and a height of about 52 μm. With thesedimensions, the minimum aspect ratio of the islands is 1.04, and theoverall aspect ratio is in the range 0.92-0.21. The aspect ratio couldbe further reduced by increasing the width of the islands. In anotherexample, for a microfluidic device having curved channels, the islandstructures may have an irregular shape with a w_(min) in the range ofabout 42-80 μm, Ain the range of about 18,000-61,000 μm², and a heightof 52 μm. With these dimensions, the minimum aspect ratio of the islandsis in the range 1.24-0.65, and the overall aspect ratio is in the range0.34-0.19.

In both cases, the low aspect ratio of the structures enablesstraightforward fabrication of molded PDMS and epoxy devices, as well asinjection molded plastic devices. This is a major advantage of thisclass of devices: they are not only extremely useful from a functionalperspective, but they also are fundamentally scalable and economicalfrom a commercial perspective.

Microfluidic Device Dimensions

For generally spherical particles being transported through amicrofluidic device having at least two channels separated by an arrayof island structures, with gaps between adjacent islands (see, e.g.,FIG. 1), the depth (e.g., as measured along the x-direction in FIG. 1)and width (e.g., as measure along the y-direction in FIG. 1) of eachmicrofluidic channel is preferably in the range of about 2 times toabout 50 times the diameter of a single particle. With respect to therigid structures that form the gaps through which fluid is extracted,the width of the structures may be up to about 10 times the width of thea single microfluidic channel, whereas the length of the structures maybe between about 0.25 times the channel width up to about 50 times thechannel width.

As an example, for a generally spherical particle having a diameter ofabout 8 microns, a microfluidic device having two microfluidic channelsseparated by an array of rigid structures similar to the configurationshown in FIG. 1 may have the following parameters: each microfluidicchannel may have a depth about 52 μm, each microfluidic channel may havea range of widths between about 10 μm to about 5000 μm, each islandstructure may have a width of about 50 μm, each island structure mayhave a length of about 200 μm.

Other examples of dimensions are set forth as follows.

For instance, the distance between the outer walls of the areacontaining the different fluid flow regions, i.e., as measuredtransverse to the fluid flow direction, can be configured to be betweenabout 1 μm to about 100 mm (e.g., about 10 μm, about 50 μm, about 100μm, about 500 μm, about 1 mm, about 5 mm, about 10 mm, or about 50 mm).Other sizes are possible as well. The width of each fluid flowregion/channel (e.g., the width of second and first microfluidicchannels 106 and 108 in FIG. 1), measured transverse to the fluid flowdirection, can be configured to be between about 1 μm to about 10 mm(e.g., about 50 μm, about 100 μm, about 250 μm, about 500 μm, about 750μm, about 1 mm, or about 5 mm). Other distances are possible as well.

The length of the gaps/openings between the island structures, asmeasured along the fluid flow direction (e.g., along the z-direction inFIG. 1), can be configured to be between about 500 nm to about 1000 μm(e.g., about 1 μm, about 2 μm, about 5 μm, about 10 μm, about 50 μm,about 100 μm, about 200 μm, about 500 μm, or about 750 μm). In someimplementations, the length of each successive opening is greater thanor less than the length of the last opening. For example, in a channelconfigured to have a decreasing fluidic resistance along the fluidpathway, each successive opening may be larger so that a greater amountof fluid is extracted through the opening. The island structures thatseparate different fluid flow regions can be configured to have amaximum length between about 10 nm to about 10 μm, and a maximum widthbetween about 10 nm to about 10 μm. Other dimensions for the gaps andisland structures are possible as well.

The height of the fluid flow regions and the island structures withinthe particle shifting area (e.g., as measured along the x-direction inFIG. 1) are within the range of approximately 100 nm to approximately 10mm. For example, the height of the channel can be about 500 nm, about 1μm, about 5 μm, about 10 μm, about 50 μm, about 100 μm, about 500 μm,about 750 μm, about 1 mm, or about 5 mm. Other heights are possible aswell. The microfluidic flow regions can have a cross-sectional area thatfalls, e.g., within the range of about 1 μm² to about 100 mm².

Microfluidic Systems

In some implementations, the particle shifting areas of the microfluidicdevices described herein are part of a larger, optional, microfluidicsystem having a network of microfluidic channels. Such microfluidicsystems can be used to facilitate control, manipulation (e.g.,separation, segregation, mixing, focusing, concentration), and isolationof liquids and/or particles from a complex parent specimen. During theisolation process, microfluidic elements provide vital functions, forexample, handling of biological fluids or reproducible mixing ofparticles with samples.

For example, the microfluidic system may include additional areas forseparating particles according to size and/or shape using othertechniques different from inertial lift forces. These other techniquesinclude, for example, deterministic lateral displacement. Theseadditional areas may employ an array of a network of gaps, in which afluid passing through a gap is divided unequally into subsequent gaps.The array includes a network of gaps arranged such that fluid passingthrough a gap is divided unequally, even though the gaps may beidentical in dimensions. In contrast to the techniques described hereinfor separating particles based on a combination of inertial lift forcesand fluid extraction, deterministic lateral displacement relies onbumping that occurs when the particle comes into direct contact withposts forming the gaps. The flow of the fluid is aligned at a smallangle (flow angle) with respect to a line-of-sight of the array.Particles within the fluid having a hydrodynamic size larger than acritical size migrate along the line-of-sight in the array, whereasthose having a hydrodynamic size smaller than the critical size followthe flow in a different direction. Flow in the device generally occursunder laminar flow conditions. In the device, particles of differentshapes may behave as if they have different sizes. For example,lymphocytes are spheres of ˜5 μm diameter, and erythrocytes arebiconcave disks of ˜7 μm diameter, and ˜1.5 μm thick. The long axis oferythrocytes (diameter) is larger than that of the lymphocytes, but theshort axis (thickness) is smaller. If erythrocytes align their long axesto a flow when driven through an array of posts by the flow, theirhydrodynamic size is effectively their thickness (˜1.5 μm), which issmaller than lymphocytes. When an erythrocyte is driven through an arrayof posts by a hydrodynamic flow, it tends to align its long axis to theflow and behave like a ˜1.5 μm-wide particle, which is effectively“smaller” than lymphocytes. The area for deterministic lateraldisplacement may therefore separate cells according to their shapes,although the volumes of the cells could be the same. In addition,particles having different deformability behave as if they havedifferent sizes. For example, two particles having the undeformed shapemay be separated by deterministic lateral displacement, as the particlewith the greater deformability may deform when it comes into contactwith an obstacle in the array and change shape. Thus, separation in thedevice may be achieved based on any parameter that affects hydrodynamicsize including the physical dimensions, the shape, and the deformabilityof the particle.

Additional information about microfluidic channel networks and theirfabrication can be found, for example, in U.S. Patent App. PublicationNo. 2011/0091987, U.S. Pat. Nos. 8,021,614, and 8,186,913, each of whichis disclosed herein by reference in its entirety.

In some implementations, a microfluidic system includes components forpreparing a particle carrying fluid sample prior to introducing thefluid into a particle shifting area. For instance, FIG. 8 is a schematicthat illustrates an example of a microfluidic system 800 that includes aparticle focusing area 801 (labeled “Concentrating units”), similar tothe particle focusing area shown in FIG. 5 that relies on inertialfocusing and siphoning/fluid extraction for increasing particle to fluidconcentration and/or for obtaining a low particle concentration fluid.The system 800 additionally includes a filter section 803 (labeled“Filter”) and a particle focusing section 805 (labeled “Focusing Units”)upstream from the particle shifting area 801. The filter section 803includes an arrangement of multiple different-sized post structures.

Based on the arrangement of the structures, the filter section 803 isconfigured to filter particles contained in an incoming fluid accordingto the particle size (e.g., average diameter), such that only particlesof a pre-defined size or less are able to pass to the next stage of thesystem 800. For instance, for complex matrices, such as bone marrowaspirate, the filter section 803 may be configured to remove bone chipsand fibrin clots to improve the efficiency of enhancing concentrationdownstream. In an example arrangement, the filter section 803 mayinclude an array of posts having a pillar size and array offset designedto deflect particles above a certain size, thereby separating them fromthe main suspension. Typically, the size limit is determined based onthe maximum particle size that can pass through later stages of thesystem 800. For example, the filter 803 may be configured tofilter/block passage of particles that have an average diameter greaterthan 50%, greater than 60%, greater than 70%, greater than 80% orgreater than 90% of the minimum width of a channel in the particleshifting area 801.

The filter section 803 is fluidly coupled to the particle focusingsection 805. The particle focusing section 805 is configured topre-focus particles exiting the filter section 803 to a desired fluidstreamline position, before the particles are provided to the particleshifting area 801. An advantage of pre-focusing the particles is that itreduces the distribution of particles across the channel width to anarrow lateral extent. The focused line of particles then can berepositioned so that the probability of the particles inadvertentlyentering the wrong channel (e.g., the channel for obtaining “filtered”fluid in the particle shifting area 801) is reduced. Pre-focusing can beachieved using inertial focusing techniques. Further details of inertialfocusing are described above in the section entitled “Particle ShiftingUsing Inertial Focusing.”

Once the particle to fluid concentration has been increased in theparticle shifting area 801, the “filtered” fluid and/or the particlesmay be coupled to a separate processing region of the microfluidicsystem 800 or removed from the system 800 for additional processingand/or analysis. For example, the second channel of the particleshifting area 801 is coupled to a first outlet 807, whereas the firstchannel of the particle shifting area 801 is coupled to a second outlet809.

External Forces

Other functionality may be added to the microfluidic system to enhancethe focusing, concentrating, separating, and/or mixing of particles. Forinstance, in some implementations, additional forces may be introducedwhich result in target specific modification of particle flow. Theadditional force may include, for example, magnetic forces, acousticforces, gravitational/centrifugal forces, electrical forces, and/orinertial forces.

FIGS. 9A-9C are schematics illustrating three different examples ofmicrofluidic devices that rely on magnetophoresis used together with theparticle shifting techniques described herein to focus different typesof particles along different corresponding streamlines within amicrofluidic device. In general, magnetophoresis employs high magneticfield gradients for sorting magnetically labeled particles flowingwithin a microfluidic channel of a device. The magnetic field gradientsare produced by placing one or more magnets adjacent to the microfluidicchannel, in which the configuration of the magnets gives rise to amagnetic flux gradient profile that extends across the microfluidicchannel. The magnetically labeled particles are subsequently “pulled” bythe gradient. Depending on the positioning of the gradient profile, themagnetically labeled particles can be focused to one or more desiredpositions within the microfluidic channels. Further details on theapplication of magnetophoresis to microfluidic devices can be found, forexample, in WO 2014/004577, incorporated herein by reference in itsentirety.

In the first example shown in FIG. 9A, a microfluidic device 900 aincludes a particle shifting area 901 fluidly coupled to magnetophoresisarea 703. The particle shifting area (labeled “Focusing” in FIG. 9A) 901is constructed in a similar manner as the device 100 shown in FIG. 1.Briefly, the focusing area 901 includes two separate fluid flow regions:a second fluid flow region and a first fluid flow region separated by a1D array of island structures, each of which is separated from anadjacent island structure by a gap. As fluid propagates through thefirst flow region, a portion of the fluid is extracted into the secondflow region, while an inertial lift force is exerted on the particles,which keeps the particles traveling within the first flow region. Ofcourse, other forces (such as inertial focusing) may be used in additionor as an alternative to keep particles within the first fluid flowregion. Both the second and first fluid flow regions of the particleshifting area are fluidly coupled into the magnetophoresis area 903,which is void of island structures.

The magnetophoresis area 903 is configured to include a magnetic fieldgradient that extends across the microfluidic channel. For example, themicrofluidic device 900 a may include one or more magnets 907 adjacentto the magnetophoresis area 903, in which the magnets 907 create themagnetic field gradient. For ease of illustration, the magnets 907 areshown at the bottom of the page to indicate their position relative tothe microfluidic devices (900 a, 900 b, and 900 c) along thelongitudinal direction of fluid flow. However, it should be understoodthat in operation, the magnets 907 are more likely to be positionedabove and/or below the fluidic channel in the magnetophoresis area 903(i.e., along the x-axis in FIGS. 9A-9C) of each of the devices 900 a,900 b and 900 c.

Referring again to FIG. 9A, two different types of particles areincluded in the fluid introduced into the focusing area 901. A firsttype of particle may include a desired analyte (e.g., a cell, platelet,or bacteria) that is bound to a magnetic marker such as a magnetic bead.The second type of particle may include a second analyte that has nosubstantial magnetic component. As the two different types of particlespass through the focusing area 901, the particles are concentrated inthe first fluid flow region and are focused along a fluid streamline.The focused particles then pass into the magnetophoresis area 903, wherethe magnetic field gradient exerts a force on the particles bound to themagnetic beads. The force generated by the interaction of the fieldgradient with the magnetic beads causes the magnetically labeledparticles to deviate from the propagation direction of the originalfluid streamline. In particular, the magnetically labeled particlesfollow the magnetic gradient and form a new stream of particles. Thedirection of the magnetic gradient, and thus the path that themagnetically labeled particles follow may depend on the orientation andarrangement of the magnets 907 near the magnetophoresis area 903. Thetwo different streams of particles, i.e., a stream containingmagnetically labeled particles and a stream of non-magnetically labeledparticles, then may be separately collected at an output of themagnetophoresis area 903 (referred to as “labeled particles” and“unlabeled particles” in FIG. 9A).

In the second example shown in FIG. 9B, the particle shifting area isconstructed in a similar manner as the device 200 in FIG. 2. Again, afluid containing a first type of particle that is bound to a magneticmarker and a second type of particle that has no substantial magneticcomponent is introduced into the focusing area 901. The fluid shiftingand inertial lift forces (or, e.g., inertial focusing forces) focus bothtypes of particles within a first fluid flow region between two arraysof island structures. The focused particles then exit the particleshifting area and are fluidly coupled into the microfluidic channel ofthe magnetophoresis area 903. Once the particles enter themagnetophoresis area 903, the magnetic field gradient generated by themagnets 907 exerts a force on the magnetically labeled particles,causing them to diverge from the propagation direction of the originalfocused stream. In the example of FIG. 9B, the stream of particlesflowing from the focusing area 901 include a first set of magneticallylabeled particles, a second set of magnetically labeled particles, and athird set of non-labeled particles. As shown in FIG. 9B, the gradient isarranged such that the magnetically labeled particles are deflectedeither to the top or bottom of the channel, whereas the non-labeledparticles continue to follow their original focused trajectory throughthe magnetophoresis area 703. Again, the labeled and unlabeledparticles, once separated, may be collected at an output of themagnetophoresis area 903 for extraction or further analysis.

The third example shown in FIG. 9C demonstrates sorting of particles ina manner opposite to that of FIG. 9B. The focusing area 901 in FIG. 9Cis constructed in a similar manner to the device 300 shown in FIG. 3. Inparticular, the focusing area 901 includes an initial island structureconfigured to separate an incoming fluid containing magnetically labeledand non-labeled particles into two separate channels (i.e., a secondfluid channel (upper channel in FIG. 9C) and a third fluid channel(lower channel in FIG. 9C), where the particles are focused intostreamlines. Once the focused streams of particles pass into themicrofluidic channel of the magnetophoresis area 903, the magnetic fieldgradient generated by the magnets 907 causes the magnetically labeledparticles to diverge towards the center of the first channel (centerchannel in FIG. 9C) and form a third focused stream. After deflection bythe magnetic gradient, the second and third streams are left withunlabeled particles. Again, both the unlabeled and labeled particles,once separated, may be collected at an output of the magnetophoresisarea 903 for extraction or further analysis.

While the examples shown in FIGS. 9A-9C perform the focusing andmagnetic separation of particles in separate stages, such functions canbe performed in a single stage. FIGS. 9D-9F are schematics illustratingthree different examples of microfluidic devices (900 d, 900 e, 9000that rely on the use of magnetophoresis with the particle shiftingtechniques described herein to focus different types of particles alongdifferent corresponding streamlines in a single stage. Again, themicrofluidic devices 900 include one or more magnets 907 to create themagnetic field gradient. The magnets 907 in FIGS. 9D-9F are shown at thebottom of the page to indicate their position relative to themicrofluidic devices (900 d, 900 e, and 9000 along the longitudinaldirection of fluid flow. However, it should be understood that inoperation, the magnets 907 are more likely to be positioned above and/orbelow the fluidic channel in the magnetophoresis area 903 (i.e., alongthe x-axis in FIGS. 9D-9F) of each of the devices 900 d, 900 e, and 900f.

Referring to FIG. 9D, the focusing area is constructed in a similarmanner as the device 100 shown in FIG. 1. That is, the focusing areaincludes a second microfluidic channel separated from a firstmicrofluidic channel by an array of island structures. In contrast toFIGS. 9A-9C, the magnetic field gradient from the magnets 907 extendsacross both the second and first fluid flow regions of the focusingarea. When a fluid containing both magnetically labeled particles andunlabeled particles is introduced into the particle shifting area, theparticles are initially constrained within the first microfluidicchannel due to inertial lift forces. However, the magnetically labeledparticles may experience a force (depending on the arrangement of themagnetic field gradient) from the magnetic field that overcomes theinertial lift force. In certain implementations, the magneticallygenerated force may cause the labeled particles to diverge from thestream of unlabeled particles and pass through openings between theisland structures.

FIGS. 9E-9F are schematics illustrating alternative configurations ofmicrofluidic devices that combine particle shifting areas withmagnetophoresis. Similar to the example of FIG. 9D, the examples shownin FIGS. 9E-9F illustrate how a magnetic field gradient can causemagnetically labeled particles to diverge from an initially focusedstream of particles and form new focused particles streams. In FIG. 9E,magnetically labeled particles are deflected through openings betweenisland structures to a second (upper channel in FIG. 9E) and third(lower channel in FIG. 9E) microfluidic channel, whereas a focusedstream of non-labeled particles remain within a first (center channel inFIG. 9E) microfluidic channel that is located between the two arrays ofisland structures. In FIG. 9F, the inertial lift forces near the islandstructures maintain the non-labeled particles along focused streamswithin a second (upper channel in FIG. 9F) and third (lower channel inFIG. 9F) microfluidic channel. In contrast, a magnetic field gradientgenerated by the magnets 907 causes magnetically labeled particles topass through openings in the island structures into a centermicrofluidic channel that is located between the second and thirdmicrofluidic channels.

The magnetic markers used for labeling particles can include sphericalbead-like materials having one or more inner magnetic cores and an outercoating, e.g., a capping polymer. The magnetic cores can be monometallic(e.g., Fe, Ni, Co), bimetallic (e.g., FePt, SmCo, FePd, and FeAu) or canbe made of ferrites (e.g., Fe₂O₃, Fe₃O₄, MnFe₂O₄, NiFe₂O₄, CoFe₂O₄). Themagnetic markers can be nanometers or micrometers in size, and can bediamagnetic, ferromagnetic, paramagnetic, or superparamagnetic, in whichsize corresponds to an average diameter or average length. For example,the magnetic markers can have a size of approximately 1 μm,approximately 600 nm, approximately 500 nm, approximately 300 nm,approximately 280 nm, approximately 160 nm, or approximately 100 nm.Other marker sizes are possible as well. The outer coating of a markercan increase its water-solubility and stability and also can providesites for further surface treatment with binding moieties. The magneticmarkers each have a magnetic moment in the range of about 1 KA/m toabout 100 kA/m. For example, in some implementations, the magneticmarkers have a magnetic moment of about 35 kA/m

In general, the magnetic markers may be bound to target analytes in afluid using binding moieties. A binding moiety is a molecule, syntheticor natural, that specifically binds or otherwise links to, e.g.,covalently or non-covalently binds to or hybridizes with, a targetmolecule, or with another binding moiety (or, in certain embodiments,with an aggregation inducing molecule). For example, the binding moietycan be a synthetic oligonucleotide that hybridizes to a specificcomplementary nucleic acid target. The binding moiety can also be anantibody directed toward an antigen or any protein-protein interaction.Also, the binding moiety can be a polysaccharide that binds to acorresponding target. In certain embodiments, the binding moieties canbe designed or selected to serve, when bound to another binding moiety,as substrates for a target molecule such as enzyme in solution. Bindingmoieties include, for example, oligonucleotides, polypeptides,antibodies, and polysaccharides. As an example, streptavidin has foursites (binding moieties) per molecule that will be recognized by biotin.For any given analyte, e.g., a specific type of cell having a specificsurface marker, there are typically many binding moieties that are knownto those of skill in the relevant fields.

For example, certain labeling methods and binding moiety techniques arediscussed in detail in U.S. Pat. No. 6,540,896 entitled,“Microfabricated Cell Sorter for Chemical and Biological Materials”filed on May 21, 1999; U.S. Pat. No. 5,968,820 entitled, “Method forMagnetically Separating Cells into Fractionated Flow Streams” filed onFeb. 26, 1997; and U.S. Pat. No. 6,767,706 entitled, “Integrated ActiveFlux Microfluidic Devices and Methods” filed on Jun. 5, 2001.

The surface of the magnetic markers can be treated to present functionalgroups (e.g., —NH₂, —COOH, —HS, —C_(n)H_(2n-2)) that can be used aslinkers to subsequently attach the magnetic markers to the targetanalytes (e.g., antibodies, drugs). In some cases, the surface treatmentmakes the magnetic markers essentially hydrophilic or hydrophobic. Thesurface treatment can include the use of polymers including, but notlimited to, synthetic polymers such as polyethylene glycol or silane,natural polymers, derivatives of either synthetic or natural polymers,and combinations thereof.

In some implementations, the surface treatment does not result in acontinuous film around the magnetic marker, but results in a “mesh” or“cloud” of extended polymer chains attached to and surrounding themagnetic marker. Exemplary polymers include, but are not limited to,polysaccharides and derivatives, such as dextran, pullanan,carboxydextran, carboxmethyl dextran, and/or reduced carboxymethyldextran, PMMA polymers and polyvinyl alcohol polymers. In someimplementations, these polymer coatings provide a surface to whichtargeting moieties and/or binding groups can bind much easier than tothe marker. For example, in some embodiments magnetic markers (e.g.,iron oxide nanoparticles) are covered with a layer of 10 kDa dextran andthen cross-linked with epichlorohydrin to stabilize the coating and formcross-linked magnetic markers.

Additional information on the fabrication, modification, and use ofmagnetic markers can be found, for example, in PCT Pub. No.WO/2000/061191, U.S. Patent App. Pub. No. 20030124194, U.S. Patent App.Pub. No. 20030092029, and U.S. Patent App. Pub. No. 20060269965, each ofwhich is incorporated herein by reference in its entirety.

Fabrication of Microfluidic Devices

A process for fabricating a microfluidic device according to the presentdisclosure is set forth as follows. A substrate layer is first provided.The substrate layer can include, e.g., glass, plastic or silicon wafer.An optional thin film layer (e.g., SiO₂) can be formed on a surface ofthe substrate layer using, for example, thermal or electron beamdeposition. The substrate and optional thin film layer provide a base onwhich microfluidic regions may be formed. The thickness of the substratecan fall within the range of approximately 500 μm to approximately 10mm. For example, the thickness of the substrate 210 can be 600 μm, 750μm, 900 μm, 1 mm, 2 mm, 3 mm, 4 mm, 5 mm, 6 mm, 7 mm, 8 mm, or 9 mm.Other thicknesses are possible as well.

After providing the substrate layer, the microfluidic channels formedabove the substrate layer. The microfluidic channels include thedifferent fluid flow pathways of the particle shifting area, as well asthe other microfluidic components of the system, including any filteringsections, inertial focusing sections, and magnetophoresis sections.Microfluidic channels for other processing and analysis components of amicrofluidic device also may be used. The microfluidic channels andcover are formed by depositing a polymer (e.g., polydimethylsiloxane(PDMS), polymethylmethacrylate (PMMA), polycarbonate (PC), or cycloolefin polymer (COP)) in a mold that defines the fluidic channelregions. The polymer, once cured, then is transferred and bonded to asurface of the substrate layer. For example, PDMS can be first pouredinto a mold (e.g., an SU-8 mold fabricated with two stepphotolithography (MicroChem)) that defines the microfluidic network ofchannels. The PDMS then is cured (e.g., heating at 65° C. for about 3hours). Prior to transferring the solid PDMS structure to the device,the surface of the substrate layer is treated with O₂ plasma to enhancebonding. Alternatively, the microfluidic channels and cover can befabricated in other materials such as glass or silicon.

Applications

The new microfluidic techniques and devices described herein can be usedin various different applications.

Centrifugation Replacement

The particle shifting techniques and devices disclosed herein can beused as replacements for centrifugation. In general, centrifugation isunderstood to include the concentrating of sub-components within a fluidthrough the application of centrifugal forces to the fluid. Typically,this process requires devices that have moving parts, which are prone towear and breakage. Moreover, the moving parts require complex and costlyfabrication processes. Another problem with centrifugation is that it isa process typically applied in a closed system, i.e., centrifugationrequires manually transferring samples to and from a centrifuge.

In contrast, the presently disclosed techniques are capable ofsubstantially increasing the concentration of fluid components usingrelatively simple micro-structures without the need for moving parts.The techniques can be implemented as part of a single open microfluidicsystem, such that fluid samples may be transferred to or from theparticle shifting area without manual interference. Additionally,particle shifting can be extended to devices requiring large throughput(i.e., volume rate of fluid that can be processed). For example, thedevices disclosed herein may be configured to enable up to 10, 25, 50,75, 100, 250, 500, 1000, 5000, or 10000 μl/min of fluid flow. Other flowrates are also possible. For instance, using device 100 in FIG. 1 as anexample, if the second and first microfluidic channels 106, 108 havedepths of approximately 50 μm and widths of approximately 50 μm, thedevice 100 may be capable of achieving a combined sample flow rate of upto about 5 mL/min. Varying the channel sizes may alter the maximumvolumetric flow rate of which the device is capable. Furthermore,multiplexing multiple channels may enable even higher rates of flow.Thus, in certain implementations, the particle shifting techniques mayprovide substantial cost and time saving advantages over traditionalcentrifugation processes. Examples of applications where a microfluidicreplacement for a centrifuge device may be useful include bone marrowand urine analysis.

Detecting Infectious Agents

In addition, the particle shifting techniques disclosed herein can beused as part of a research platform to study analytes of interest (e.g.,proteins, cells, bacteria, pathogens, and DNA) or as part of adiagnostic assay for diagnosing potential disease states or infectiousagents in a patient. By separating and focusing particles within a fluidsample, the microfluidic device described herein may be used to measuremany different biological targets, including small molecules, proteins,nucleic acids, pathogens, and cancer cells. Further examples aredescribed below.

Rare Cell Detection

The microfluidic device and methods described herein may be used todetect rare cells, such as circulating tumor cells (CTC) in a bloodsample or fetal cells in blood samples of pregnant females. For example,the concentration of primary tumor cells or CTCs can be enhanced in ablood sample for rapid and comprehensive profiling of cancers. Bycombining the particle deflection techniques described herein withmagnetophoresis (see FIG. 7), different types of cells can be detected(e.g., circulating endothelial cells for heart disease). Thus, themicrofluidic device may be used as a powerful diagnostic and prognostictool. The targeted and detected cells could be cancer cells, stem cells,immune cells, white blood cells or other cells including, for example,circulating endothelial cells (using an antibody to an epithelial cellsurface marker, e.g., the Epithelial Cell Adhesion Molecule (EpCAM)), orcirculating tumor cells (using an antibody to a cancer cell surfacemarker, e.g., the Melanoma Cell Adhesion molecule (CD146)). The systemsand methods also can be used to detect small molecules, proteins,nucleic acids, or pathogens.

Fluid Exchange

The microfluidic device and methods described herein may be used toshift cells from one carrier fluid to another carrier fluid. Forexample, the particle shifting techniques disclosed could be used toshift cells into or out of a fluid stream containing reagents, such asdrugs, antibodies, cellular stains, magnetic beads, cryoprotectants,lysing reagents, and/or other analytes.

A single particle shifting region could contain many parallel fluidstreams (from many inlets) through which a shifted cell would pass. Forexample, white blood cells could be shifted from a blood stream into astream containing staining reagents and then into a buffer stream.

In bioprocessing and related fields, the devices and techniquesdescribed may be used to enable sterile, continuous transfer of cellsfrom old media (containing waste products) into fresh growth media.Similarly, extracellular fluids and cellular products (e.g., antibodies,proteins, sugars, lipids, biopharmaceuticals, alcohols, and variouschemicals) may be extracted from a bioreactor in a sterile, continuousmanner while cells are retained within the bioreactor.

Fluid Sterilization and Cleansing

The microfluidic device microfluidic device and methods described hereinmay be used to remove pathogens, pollutants, and other particularcontaminants from fluids. By shifting contaminants across fluidstreamlines, contaminants may be removed from a fluid sample andcollected as a separate waste stream.

Harvesting Algae for Biofuels

Harvesting algae from growth media is a major expense in the productionof biofuels because algae grow in very dilute suspensions at nearneutral buoyancy, making efficient extraction and concentration of algalbiomass difficult. The microfluidic device and methods described hereincan provide an efficient means of harvesting algae that does not dependon either density or filtration. The devices and techniques describedenable the algae in a growth tank to be extracted from the growth mediaand concentrated to a high volume density. This can be done either as asingle step or as part of a continuous process. Additionally, becausethe devices described herein can sort cells in a size-dependent manner,they can be designed to sort and concentrate only the larger algae thathave reached maturity, returning smaller, immature algae to the growthtank.

EXAMPLES

The invention is further described in the following examples, which donot limit the scope of the invention described in the claims.

Device Fabrication

Various experiments were performed to analyze the behavior ofmicrofluidic devices having asymmetrically curved channels (see, e.g.,the section above entitled “Increasing Particle Concentration/ReducingFluid Volume” and the device shown in FIG. 5) that combine inertialfocusing with fluid extraction to achieve volume reduction ofparticle-rich fluid samples. That is, the devices included a focusingchannel (see, e.g., channel 508 in FIG. 5) in which particles werefocused using inertial focusing techniques and a particle-freechannel/second fluid flow channel (see, e.g., channel 506 in FIG. 5)into which fluid from the focusing channel was extracted. Theexperiments are described in Examples 1 to 5 below. The devices used inthose examples were designed and fabricated as follows.

For each microfluidic device, standard SU8 photolithography and softlithography techniques were used to fabricate the master mold and thePDMS microchannels, respectively. Briefly, negative photoresist SU8-50(Microchem Corp, Massachusetts) was spun at 2850 RPM to a thickness ofapproximately 50 μm, exposed to ultraviolet light through a mylaremulsion printed photomask (Fineline Imaging, Colorado) that defines themicrofluidic network of channels, and developed in BTS-220 SU8-Developer(J.T. Baker, New Jersey) to form a raised mold. A 10:1 ratio mixture ofSylgard 184 Elastomer base and curing agent (Dow Corning, Michigan) wasthen poured over the raised mold, allowed to cure in an oven at 65° C.for 8 hours and then removed from the SU8 master mold to form themicrofluidic device cover having the patterned channels. Inlet andoutlet holes to the channels were punched using custom sharpened needletips. The devices were then cleaned of particulate using low-residuetape and oxygen plasma bonded to pre-cleaned 1 mm thick glass microscopeslides.

For experiments where high pressure deformation of PDMS was a concern,epoxy devices were used instead. Epoxy devices were constructed usingPDMS molds created by treating PDMS channels withtridecafluoro-1,1-2,2-tetrahydrooctyl-trichlorosilane (Gelest) and thenpouring PDMS over the silanized channels. After 24 hours of curing at65° C., the molds were carefully separated from the silanized channels.Holes were punched into PDMS molds at the inlets and outlets using a0.75 mm diameter Harris Uni-Core biopsy punch. Teflon coated wire (0.028inch diameter, McMaster-Carr) was inserted gently into these holes as tonot deform the surface of the PDMS mold. Tygon tubing (0.02″ I.D., 0.06″O.D.) was then guided onto teflon coated wire and suspended ˜1 mm fromthe mold surface. Epoxacast 690 (Smooth-On) was mixed and degassed for30 minutes prior to pouring into the mold. At the same time as moldswere filled, slides were coated with epoxy by laying a glass slide on adrop of epoxy atop a flat PDMS surface. After ˜28 hours, the deviceswere cooled temporarily to ˜22° C. to prevent deformation, the Teflonwire was removed and devices removed from the molds. Then the glassslides were removed from the PDMS slabs and heated to 55° C. and deviceswere pressed against slides ensuring bonding.

Particle and Cell Suspensions

The devices used in the Examples described below were tested over a widerange of flow conditions using fluorescent polystyrene beads and whiteblood cells as exemplar particles. Polystyrene particle suspensions werecreated using 4.4 μm diameter blue-fluorescent beads (Polysciences), 9.9μm diameter green-fluorescent beads (ThermoFisher Scientific) and 15 μmdiameter red-fluorescent beads (Invitrogen). Each was suspended to afinal length fraction of 0.1 in an equivalent density solution (1.05g/mL) of 1×PBS, 0.1% Tween20, and iodixanol. White blood cells (buffycoat) were isolated using deterministic lateral displacement with aco-flow of buffer solution.

Fluorescent Counting and Cell Counting Fluorescent and high resolutionimaging of fluid samples were accomplished using an automated Nikon TiEinverted microscope with a Retiga 2000R monochromatic camera as well asa Vision Research Phantom v4.2 high speed monochromatic camera.

Hemocytometers and Nageotte chambers were utilized for measuringparticle concentrations in white blood cell yield experiments atdilutions dependent upon the output cell concentrations.

Example 1: Cell Free Layer Growth and Siphon Percentage

The combined siphoning and inertial focusing design takes advantages offast-acting inertial forces, which generate a particle-free layer nearthe walls of the microfluidic channel. This particle-free fluid layerthen is controllably siphoned off leaving the particles once againcloser to the walls where the inertial forces are strongest. The processof focusing and siphoning may be repeated until a desired volumereduction is achieved. When using a microfluidic device to enhance theconcentration of particles within a fluid or to extract a particle-freefluid, an important design consideration may include controlling thepercentage of fluid that is siphoned relative to the dynamics of theformation of the particle-free layer. In inertial focusing systems, thefocusing behavior is a cumulative result of numerous parametersincluding the channel geometry as well as flow speed (See, e.g., DiCarlo, D. “Inertial microfluidics,” Lab Chip 9, 3038 (2009) and Martel,J. & Toner, M. “Inertial Focusing in Microfluidics,” Annual Review ofBiomedical Engineering 16, 371-396 (2014), incorporated herein byreference in their entirety). For instance, curved structures aregenerally more efficient than planar structures at achieving focusingover a given channel length while in some implementations are also moresensitive to changes in flow speed.

Using asymmetrically curved structures similar to the structuresdescribed with respect to FIGS. 5-6, we characterized the formation of aparticle-free layers for a range of focusing channel widths (between 50μm to 200 μm) and over a range of flow rates (between 10 μL/min and 3000μL/min) depending on the channel width. Each of the devices testedincluded a series of five focusing-siphoning unit pairs (see, e.g., FIG.6) followed by an expansion into a 500 μm wide straight section. Theparticle-free layer width of the resulting output fluid was measureddownstream of the focusing units after the channel had fully expandedbased on a 10% relative intensity threshold across the channel width(i.e., the intensity is normalized to between 0% to 100%, after whichthe position at which the intensity reaches 10% is identified. See,e.g., Martel, J. M. & Toner, M. “Particle Focusing in CurvedMicrofluidic Channels,” Sci. Rep. 3, 1-8 (2013), incorporated herein byreference in its entirety).

The width of the particle-free layer at the optimal flow rate for eachchannel width was compared to one another as shown in FIG. 10.Specifically, FIG. 10 shows the “cell-free fraction” versus flow rate,in which each of the data points represents the maximum fraction of thefluid (as measured across the channel width) that is free of particlesfor each different sized channel. The legend beneath the plot indicatesthe channel widths. As is evident from the graph shown in FIG. 10, thenarrower channels achieve significantly higher maximum particle-freelayer width than the wider channels (50 μm wide-38%, 75 μm-46%, 100μm-42%, 125 μm-30%, 150 μm-15%, 200 μm-13%). The variation inparticle-free layer width over a range +/−50% of the optimal flow rate(flow rate which achieves the maximum particle-free layer width) waslower for the wider channels (50 μm wide-12%, 75 μm-23%, 100 μm-16%, 125μm-15%, 150 μm-4.6%, 200 μm-5.5%).

Using the reference data we determined that there was a nearly linearrelationship between the optimal flow rate, Q_(Optimal) (i.e., the flowrate that resulted in the greatest width for particle-free layerformation), and the focusing unit width,w_(focus)=1.0911e⁻⁰⁷*Q_(Optimal) (μL/min)+4.4789e⁻⁰⁵ m. Based on theforegoing relationship, it is possible to create a device that maintainsa high level of particle-free layer formation efficiency as fluid issiphoned from the focusing channel and as the flow rate through thefocusing channels decreases.

The relationship between the formation of the particle-free layer and amaximum siphon percentage was also studied. The siphon percentage is thepercentage of flow in the focusing channel that is siphoned out at thenext opening between islands. The amount siphoned is determined by therelative fluidic resistances of the focusing and siphon channels. Inparticular, a set of devices was designed using a range of siphonpercentages (7%, 10%, 12% and 15%) for a fixed input flow rate of 500μL/min. The flow rate of 500 μL/min was chosen to be within the optimalflow rate range of the narrower more efficient focusing unit widths. Acomparison of the focusing performance of these devices indicates that,depending on the volume reduction factor desired, the siphon percentagemust be below 10% for a factor of 10 volume reduction and 7% for afactor of 50 volume reduction. The volume reduction factor is equivalentto the concentration factor and may be expressed as one divided by thefraction of flow in the focusing channel. For example, if 5% of thetotal flow is in the focusing channel, the volume reduction factor is20. FIG. 11 includes images of fluorescently tagged white blood cellsflowing through the focusing-siphoning units of the microfluidic device,in which each image corresponds to a different siphon percentage for afactor of 10 volume reduction. As is evident from the images, the lossof particles from the focusing channel into the second fluid flowchannel in the 15% siphon percentage device is quite noticeable.

As the foregoing results demonstrate, the combined siphoning andinertial focusing techniques enable the control of the volume reductionfactor in a well-regulated manner. In some implementations, it may bepossible to obtain a specific volume reduction factor thereby tailoringa specific sample volume for downstream molecular assays independent ofthe input sample volume.

For the experiments described below, we have selected two specificdesigns for detailed characterization. The two selected designs are afactor of 10 (“10×”) concentrator (this device included 26focusing-siphoning unit pairs and had a 10% siphon percentage) and afactor of 50 (“50×”) concentrator (this device included 152focusing-siphoning unit pairs and had a 7% siphon percentage).

Example 2: Flow Rate Dependence

Another factor that may be considered in a microfluidic system forperforming volume reduction and/or increasing the particle concentrationwithin a fluid is the flow speed of the fluid sample through themicrofluidic device. Accordingly, the sensitivity to flow rate was alsoinvestigated. Using isolated white blood cells (buffy coat), the yieldsof both the 10× and 50× devices were analyzed between input flows ratesof 100 μL/min and 1000 μL/min. Yield is calculated on a relative basisbetween the number of cells in the stream flowing in the focusingchannel and the number of cells in the second fluid flow region or,alternatively, as the total number of cells in the stream flowing in thefocusing channel divided by total cells in the focusing channel and thesecond fluid flow channel combined. A high yield of greater than 95% forthe devices was maintained between 400 and 600 μL/min but beyond thatthe drop off in yield began to be significant. For instance, multipleseparate streams containing the white blood cells began to form at 1000μL/min.

FIG. 12 is a plot of relative white blood cell yield versus flow ratefor both the 10× and 50× devices. In general, the system loss (e.g., dueto cells lost in transfers between various containers, in tubing, etc.)comparing the input number of cells to total cells coming out of thefocusing channel and the second flow channel combined was typically low,around 10%. For flow rates lower than 400 μL/min, the drop off in yieldwas consistent with an overall lack of focusing. For example, in thecase of negligible inertial effects, one would expect a yield equivalentto the flow split, such as 10% and 2% for the 10× and 50× devices,respectively. The increase in yield by increasing the flow rate from 100to 400 μL/min was indicative of the improvement of focusing withReynolds number as inertial effects increase. The decrease in yieldafter 600 μL/min was a likely a consequence of PDMS deformation at thehigher driving pressures leading to significantly different focusingpatterns.

The exact range of input and output flow rates depend on the particlesize and channel dimensions used. To efficiently achieve higherthroughput for a given design, multiplexing of channels may be needed.

Example 3: Size Dependence

Inertial forces are strongly dependent upon the size of the particlesbeing focused. Accordingly, the performance of the combined inertialfocusing and siphoning devices were evaluated to understand thesensitivity to particle size. In particular, a variety of polystyreneparticle sizes (4 μm-10 μm) were run simultaneously through the 10× and50× devices in order to determine the size range of particles that aredeflected from the focusing channel to the second fluid flow regionwhere the “particle-free” layer was desired. FIG. 13 is a plot of theforegoing experiment and suggests a trend where smaller particle sizeshave lower relative yields (i.e., (total cells in product)/(total cellsin product+total cells in waste)) compared to larger particle sizes,i.e., the smaller a particle is, the greater the probability that theparticle will escape the focusing channel through a gap between islandstructures. If relative yields above 90% are desired, a cutoff particlesize for this threshold can be interpolated as approximately 8.5 μm forthe 10× device and approximately 8 μm for the 50× device. This slightdifference may be attributed to the significantly lower velocities atthe end of the 50× concentrator where the focusing becomes moresensitive to particle size.

The foregoing results showing the sensitivity of the combined siphoningand inertial focusing devices to particle size may lead to severalpossible advantageous applications. For instance, the size dependencecan be beneficial for cleanup of biological samples (e.g., removingbacteria) as particles smaller than a cutoff size will be siphoned offfrom the focusing channel into the second fluid flow channel, thusimproving the final sample purity or decreasing undesired biologicalsample contamination.

Example 4: Volume Fraction Dependence

Another factor that was analyzed was the effect of inter-particleinteractions on the focusing behavior. Generally, conventional inertialfocusing devices have a strict requirement that the input fluid sampleconcentrations be low in order to achieve high quality focusing (see,e.g., Lee, W., Amini, H., Stone, H. A. & Di Carlo, D. “Dynamicself-assembly and control of microfluidic particle crystals,”Proceedings of the National Academy of Sciences 107, 22413 (2010),incorporated herein by reference in its entirety). A theoreticalconcentration limitation is given by the limit of a continuous line ofadjacently touching particles at the equilibrium positions along theentire channel length or a length fraction of 1 (see, e.g., Di Carlo, D.“Inertial microfluidics,” Lab Chip 9, 3038 (2009), incorporated hereinby reference in its entirety). We investigated the operational cutoff ofthe particle concentration for the 10× and 50× devices by varying theinput concentration of white blood cells processed at 500 μL/min.

FIG. 14 is a plot illustrating the relative yield of the white bloodcells at this flow rate for different input concentrations. As the plotindicates, there is a sharp maximum limit at an input concentration ofapproximately 1 million cells per milliliter. The particle concentrationat which the particle interactions will start affecting the performanceof the device threshold was reached in the devices of approximately atapproximately 80M cells per milliliter. This high particle concentrationmay be attributable to the fact that the operational success or yield ofthe devices does not require that all of the particles fall on a singlestreamline. Instead, the cell free layer formation near the walls leadsto a much higher concentration at which the yield decreases (i.e.,rather than requiring all particles to pack into the limited space of asingle narrow stream, we only required that particles be packed into theregion of fluid that is not siphoned, which can accommodate far moreparticles). The foregoing experimental results indicate that theparticle-free layer formation is not as sensitive to particle volumefraction as the single stream or high quality inertial focusing aspreviously understood (see, e.g., Di Carlo, D. “Inertial microfluidics,”Lab Chip 9, 3038 (2009), incorporated herein by reference in itsentirety).

Example 5: Achieving Greater Than 50× Volume Reduction

We also analyzed the ability of the microfluidic volume reductiondevices to obtain substantially high throughputs and volume reduction.For example, in some cases, large numbers of the devices shown in FIGS.1-5 may be operated in parallel to increase the overall systemthroughput (i.e., the overall volume of fluid processed). For instance,in one possible design, multiple volume reduction devices (e.g., device100) may each have a separate fluid input to receive a fluid sample,where the output of each device is coupled to a common output channelfor collecting either concentrated particles or the filtered fluidsample.

Alternatively, or in addition, two or more devices may be constructed inseries so that particle concentration/volume reduction is modified ateach stage (i.e., device) of the overall system. To demonstrate theapplication of serial volume reduction, we constructed a microfluidicsystem containing serially integrated devices: in particular, we usedten parallel 10× devices that feed into a single 50× device for atheoretical overall volume reduction of 500×. FIG. 15 is a schematicthat illustrates a top view of the design of the system 1500 used tostudy volume reduction, which includes ten parallel 10× concentratordevices 1502 and a single 50× concentrator device 1504. The operation ofthe system 1500 proceeds as follows: (i) dilute particles enter thesystem 1500 and are focused in the separate 10× concentrators 1502 intoten parallel focused streams; (ii) the ten parallel focused streams thenare sent through a series of converging channels 1506; (iii) theconverged streams then are refocused as they enter the 50× device 1504;and (iv) finally, all the particles exit through the bottom productoutlet of the 50× device.

Due to the pressure requirements and PDMS deformation, the systems usedfor the experiments were fabricated in rigid epoxy in place of PDMS[Eugene J. Lim et al. “Inertio-elastic focusing of bioparticles inmicrochannels at high throughput,” Nature Communications. 2014] (see,e.g., Martel, J. M. & Toner, M. “Particle Focusing in CurvedMicrofluidic Channels,” Sci. Rep. 3, 1-8 (2013), incorporated herein byreference in its entirety). To test the yield, white blood cells at aninput concentration of 100,000 per mL were introduced into the system.The yield of the integrated system was consistently above 95% andexhibited a volume reduction factor of ˜411. Thus, for a 30 mL inputsample containing 100,000 white blood cells per mL, the sample will bereduced by the microfluidic system into 73 μL+/−1.2 μL (n=5) withgreater than 95% of the original cells (95.7%+/−3.6%, n=5). Thediscrepancy between the 411 volume reduction factor and 500 designedvolume reduction factor is a difference of only a few microliters ofproduct which was difficult to control as the input flow rate of 4mL/min (pump driving force limitation) and the product flow rate of <10μL/min. That is to say, that while the device was designed to perform500× volume reduction, it actually performed 400× volume reduction. Itis believed that the relative resistances of the product and wastechannels were slightly off, such that slightly more volume went to theproduct than desired. Additionally, the tiny product volume may havecaused some measurement error. Tiny fabrication imperfections in themicrofluidic system can alter this balance as well.

Centrifugation used for washing cells, exchanging media and/orconcentrating a sample for subsequent assays is one of the most widelyutilized processes in the biomedical sciences. The system 1500 and theforegoing experimental results demonstrate that the microfluidicsiphoning and inertial focusing devices are capable of accomplishing theforegoing common biomedical tasks typically performed withcentrifugation in a continuous flow and sterile manner at throughputs ofup to 4 mL/min (240 mL/hour) and at volume reduction factors of 20-foldor higher. Furthermore, the typical limitation on throughput ofmicrofluidic devices is also mitigated using the combined siphoning andinertial focusing techniques. While we have presented a non-integratedsingle device which achieves a throughput of 500 μL/min at a volumereduction factor of 50×, the devices can be further arranged in parallelto obtain a set of greater than 40 channels (20 mL/min or 1200 mL/hr),diminishing the run time for the larger volume samples.

While much of the advancement presented is in terms of improvingexperimental methods there has also been a key finding about the natureof inertial focusing. The realization that the particle-free layerformation is not as sensitive to particle volume fraction as the singlestream or high quality inertial focusing previously predicted may beintuitive, but also brings to light a new means of comparing inertialfocusing device performance. There are typically five differentgeometries utilized in inertial focusing and typically are each comparedby the length required to achieve a minimum streak width. By changingthe definition of optimal focusing from minimizing streak width to thedynamic formation of the particle-free layer, new insights into thedynamics of focusing for different microfluidic structures can beinvestigated and directly compared. This new means of comparison couldstandardize how the effectiveness of this class of microfluidic devicesis measured.

Other Embodiments

It is to be understood that while the invention has been described inconjunction with the detailed description thereof, the foregoingdescription is intended to illustrate and not limit the scope of theinvention, which is defined by the scope of the appended claims.

What is claimed is:
 1. A microfluidic device comprising: a first microfluidic channel; a second microfluidic channel extending along the first microfluidic channel; and a first array of islands separating the first microfluidic channel from the second microfluidic channel, wherein a boundary of the first microfluidic channel is defined by a first undulating outer wall, wherein each island is separated from an adjacent island in the array by an opening that fluidly couples the first microfluidic channel to the second microfluidic channel, wherein the first microfluidic channel, the second microfluidic channel, and the islands are arranged so that a fluidic resistance of the first microfluidic channel increases relative to a fluidic resistance of the second microfluidic channel along a longitudinal direction of the first microfluidic channel such that, during use of the microfluidic device, a portion of a fluid sample flowing through the first microfluidic channel passes through one or more of the openings between adjacent islands into the second microfluidic channel, wherein a width of the first microfluidic channel repeatedly alternates between a narrow region and an enlarged region along the longitudinal direction of the first microfluidic channel, and wherein, for each island, a contour of a first side of the island substantially matches a contour of the first undulating outer wall of the first channel facing the first side of the island such that a width between the first side of the island and a boundary of the first undulating outer wall is constant.
 2. The microfluidic device of claim 1, wherein each opening has an opening length, and each island has an island length that is greater than the opening length of an opening adjacent to the island, such that, for an average particle diameter of a first type of particle and for a fluid velocity of the fluid sample, the first microfluidic channel, the second microfluidic channel and the first array of islands are arranged to, during use of the microfluidic device, impart an inertial lift force on the first type of particles to substantially prevent the first type of particles from propagating through one or more of the openings between adjacent islands into the second microfluidic channel.
 3. The microfluidic device of claim 1, wherein a cross-sectional area of each opening through which the fluid passes from the first microfluidic channel into the second microfluidic channel is larger than the first type of particle.
 4. The microfluidic device of claim 1, wherein the increase in fluidic resistance of the first channel relative to the fluidic resistance of the second channel comprises a change in a cross-sectional area of the first microfluidic channel or the second microfluidic channel along the longitudinal direction of the first microfluidic channel.
 5. The microfluidic device of claim 4, wherein the change in cross-sectional area of the second microfluidic channel comprises an increase in the cross-sectional area of the second microfluidic channel relative to the cross-sectional area of the first microfluidic channel along the longitudinal direction.
 6. The microfluidic device of claim 4, wherein the change in cross-sectional area of the first microfluidic channel comprises a decrease in the cross-sectional area of the first microfluidic channel relative to the cross-sectional area of the second microfluidic channel along the longitudinal direction.
 7. The microfluidic device of claim 1, wherein at least one of the enlarged regions is aligned with a corresponding opening between the islands.
 8. The microfluidic device of claim 1, wherein the first microfluidic channel has an approximately sinusoidal shape.
 9. The microfluidic device of claim 1, wherein, for each island, a contour of a first side of the island substantially matches a contour of the first undulating outer wall facing the first side of the island.
 10. The microfluidic device of claim 1, wherein the first microfluidic channel, the second microfluidic channel, and the first array of islands correspond to a combined inertial focusing and fluid siphoning region, and wherein the microfluidic device comprises a plurality of combined inertial focusing and fluid siphoning regions arranged in parallel.
 11. The microfluidic device of claim 1, further comprising one or more magnets establishing a magnetic field gradient across the first and/or second microfluidic channel.
 12. A microfluidic device comprising: a first microfluidic channel; a second microfluidic channel extending along the first microfluidic channel; and a first array of islands separating the first microfluidic channel from the second microfluidic channel, wherein a boundary of the first microfluidic channel is defined by a first undulating outer wall, wherein each island is separated from an adjacent island in the array by an opening that fluidly couples the first microfluidic channel to the second microfluidic channel, wherein the first microfluidic channel, the second microfluidic channel, and the islands are arranged so that a fluidic resistance of the first microfluidic channel increases relative to a fluidic resistance of the second microfluidic channel along a longitudinal direction of the first microfluidic channel such that, during use of the microfluidic device, a portion of a fluid sample flowing through the first microfluidic channel passes through one or more of the openings between adjacent islands into the second microfluidic channel, wherein a width of the first microfluidic channel repeatedly alternates between a narrow region and an enlarged region along the longitudinal direction of the first microfluidic channel, and wherein, for each island, a contour of a first side of the island substantially matches a contour of the first undulating outer wall of the first channel facing the first side of the island, and a radii of curvature of the first undulating outer wall through a first turn of the first microfluidic channel is smaller than a radii of curvature of the first undulating outer wall through a second adjacent turn of the first microfluidic channel.
 13. The microfluidic device of claim 12, wherein each opening has an opening length, and each island has an island length that is greater than the opening length of an opening adjacent to the island, such that, for an average particle diameter of a first type of particle and for a fluid velocity of the fluid sample, the first microfluidic channel, the second microfluidic channel and the first array of islands are arranged to, during use of the microfluidic device, impart an inertial lift force on the first type of particle to substantially prevent the first type of particles from propagating through one or more of the openings between adjacent islands into the second microfluidic channel.
 14. The microfluidic device of claim 12, wherein a cross-sectional area of each opening through which the fluid passes from the first microfluidic channel into the second microfluidic channel is larger than the first type of particle.
 15. The microfluidic device of claim 12, wherein the increase in fluidic resistance of the first channel relative to the fluidic resistance of the second channel comprises a change in a cross-sectional area of the first microfluidic channel or the second microfluidic channel along the longitudinal direction of the first microfluidic channel.
 16. The microfluidic device of claim 15, wherein the change in cross-sectional area of the second microfluidic channel comprises an increase in the cross-sectional area of the second microfluidic channel relative to the cross-sectional area of the first microfluidic channel along the longitudinal direction.
 17. The microfluidic device of claim 15, wherein the change in cross-sectional area of the first microfluidic channel comprises a decrease in the cross-sectional area of the first microfluidic channel relative to the cross-sectional area of the second microfluidic channel along the longitudinal direction.
 18. The microfluidic device of claim 12, wherein at least one of the enlarged regions is aligned with a corresponding opening between the islands.
 19. The microfluidic device of claim 12, wherein the first microfluidic channel has an approximately sinusoidal shape.
 20. The microfluidic device of claim 12, wherein, for each island, a contour of a first side of the island substantially matches a contour of the first undulating outer wall facing the first side of the island.
 21. The microfluidic device of claim 12, wherein the first microfluidic channel, the second microfluidic channel, and the first array of islands correspond to a combined inertial focusing and fluid siphoning region, and wherein the microfluidic device comprises a plurality of combined inertial focusing and fluid siphoning regions arranged in parallel.
 22. The microfluidic device of claim 12, further comprising one or more magnets establishing a magnetic field gradient across the first and/or second microfluidic channel.
 23. A method of changing a concentration of particles within a fluid within a microfluidic device, the method comprising: flowing a fluid containing a plurality of particles into a microfluidic region comprising a first microfluidic channel, a second microfluidic channel extending along the first microfluidic channel, and a first array of islands separating the first microfluidic channel from the second microfluidic channel, the microfluidic region having a width that repeatedly alternates between a narrow region and an enlarged region along the longitudinal direction of the microfluidic channel, such that inertial focusing causes the plurality of particles to be focused into one or more streamlines of the fluid within the first microfluidic channel. 